Exploiting the relationship between 4-dimensional toric and semitoric integrable systems with Delzant and semitoric polygons, respectively, we develop techniques to compute certain equivariant packing densities and equivariant capacities of these systems by working exclusively with the polygons. This expands on results of Pelayo and Pelayo-Schmidt. We compute the densities of several important examples and we also use our techniques to solve the equivariant semitoric perfect packing problem, i.e., we list all semitoric polygons for which the associated semitoric system admits an equivariant packing which fills all but a set of measure zero of the manifold. This paper also serves as a concise and accessible introduction to Delzant and semitoric polygons in dimension four.
{"title":"Packing Densities of Delzant and Semitoric Polygons","authors":"Du, Yu, Kosmacher, Gabriel, Liu, Yichen, Massman, Jeff, Palmer, Joseph, Thieme, Timothy, Wu, Jerry, Zhang, Zheyu","doi":"10.3842/sigma.2023.081","DOIUrl":"https://doi.org/10.3842/sigma.2023.081","url":null,"abstract":"Exploiting the relationship between 4-dimensional toric and semitoric integrable systems with Delzant and semitoric polygons, respectively, we develop techniques to compute certain equivariant packing densities and equivariant capacities of these systems by working exclusively with the polygons. This expands on results of Pelayo and Pelayo-Schmidt. We compute the densities of several important examples and we also use our techniques to solve the equivariant semitoric perfect packing problem, i.e., we list all semitoric polygons for which the associated semitoric system admits an equivariant packing which fills all but a set of measure zero of the manifold. This paper also serves as a concise and accessible introduction to Delzant and semitoric polygons in dimension four.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136133621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We are concerned with the Umemura polynomials associated with rational solutions of the third Painlevé equation. We extend Taneda's method, which was developed for the Yablonskii-Vorob'ev polynomials associated with the second Painlevé equation, to give an algebraic proof that the rational functions generated by the nonlinear recurrence relation which determines the Umemura polynomials are indeed polynomials. Our proof is constructive and gives information about the roots of the Umemura polynomials.
{"title":"A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation","authors":"Peter A. Clarkson, Chun-Kong Law, Chia-Hua Lin","doi":"10.3842/sigma.2023.080","DOIUrl":"https://doi.org/10.3842/sigma.2023.080","url":null,"abstract":"We are concerned with the Umemura polynomials associated with rational solutions of the third Painlevé equation. We extend Taneda's method, which was developed for the Yablonskii-Vorob'ev polynomials associated with the second Painlevé equation, to give an algebraic proof that the rational functions generated by the nonlinear recurrence relation which determines the Umemura polynomials are indeed polynomials. Our proof is constructive and gives information about the roots of the Umemura polynomials.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"7 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135113060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Florio M. Ciaglia, Jürgen Jost, Lorenz J. Schwachhöfer
Jordan algebras arise naturally in (quantum) information geometry, and we want to understand their role and their structure within that framework. Inspired by Kirillov's discussion of the symplectic structure on coadjoint orbits, we provide a similar construction in the case of real Jordan algebras. Given a real, finite-dimensional, formally real Jordan algebra ${mathcal J}$, we exploit the generalized distribution determined by the Jordan product on the dual ${mathcal J}^{star}$ to induce a pseudo-Riemannian metric tensor on the leaves of the distribution. In particular, these leaves are the orbits of a Lie group, which is the structure group of ${mathcal J}$, in clear analogy with what happens for coadjoint orbits. However, this time in contrast with the Lie-algebraic case, we prove that not all points in ${mathcal J}^{*}$ lie on a leaf of the canonical Jordan distribution. When the leaves are contained in the cone of positive linear functionals on ${mathcal J}$, the pseudo-Riemannian structure becomes Riemannian and, for appropriate choices of ${mathcal J}$, it coincides with the Fisher-Rao metric on non-normalized probability distributions on a finite sample space, or with the Bures-Helstrom metric for non-normalized, faithful quantum states of a finite-level quantum system, thus showing a direct link between the mathematics of Jordan algebras and both classical and quantum information geometry.
{"title":"Information Geometry, Jordan Algebras, and a Coadjoint Orbit-Like Construction","authors":"Florio M. Ciaglia, Jürgen Jost, Lorenz J. Schwachhöfer","doi":"10.3842/sigma.2023.078","DOIUrl":"https://doi.org/10.3842/sigma.2023.078","url":null,"abstract":"Jordan algebras arise naturally in (quantum) information geometry, and we want to understand their role and their structure within that framework. Inspired by Kirillov's discussion of the symplectic structure on coadjoint orbits, we provide a similar construction in the case of real Jordan algebras. Given a real, finite-dimensional, formally real Jordan algebra ${mathcal J}$, we exploit the generalized distribution determined by the Jordan product on the dual ${mathcal J}^{star}$ to induce a pseudo-Riemannian metric tensor on the leaves of the distribution. In particular, these leaves are the orbits of a Lie group, which is the structure group of ${mathcal J}$, in clear analogy with what happens for coadjoint orbits. However, this time in contrast with the Lie-algebraic case, we prove that not all points in ${mathcal J}^{*}$ lie on a leaf of the canonical Jordan distribution. When the leaves are contained in the cone of positive linear functionals on ${mathcal J}$, the pseudo-Riemannian structure becomes Riemannian and, for appropriate choices of ${mathcal J}$, it coincides with the Fisher-Rao metric on non-normalized probability distributions on a finite sample space, or with the Bures-Helstrom metric for non-normalized, faithful quantum states of a finite-level quantum system, thus showing a direct link between the mathematics of Jordan algebras and both classical and quantum information geometry.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135617764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We apply the techniques developed in our previous article to describe some interesting families of ALF gravitational instantons with conical singularities. In particular, we completely understand the 5-dimensional family of Chen-Teo metrics and prove that only 4-dimensional subfamilies can be smoothly compactified so that the metric has conical singularities.
{"title":"About a Family of ALF Instantons with Conical Singularities","authors":"Olivier Biquard, Paul Gauduchon","doi":"10.3842/sigma.2023.079","DOIUrl":"https://doi.org/10.3842/sigma.2023.079","url":null,"abstract":"We apply the techniques developed in our previous article to describe some interesting families of ALF gravitational instantons with conical singularities. In particular, we completely understand the 5-dimensional family of Chen-Teo metrics and prove that only 4-dimensional subfamilies can be smoothly compactified so that the metric has conical singularities.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135617760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The quest for a consistent theory for quantum gravity is one of the most challenging problems in theoretical high-energy physics. An often-used approach is to describe the gravitational degrees of freedom by the metric tensor or related variables, and finding a way to quantise this. In the canonical tensor model, the gravitational degrees of freedom are encoded in a tensorial quantity $P_{abc}$, and this quantity is subsequently quantised. This makes the quantisation much more straightforward mathematically, but the interpretation of this tensor as a spacetime is less evident. In this work we take a first step towards fully understanding the relationship to spacetime. By considering $P_{abc}$ as the generator of an algebra of functions, we first describe how we can recover the topology and the measure of a compact Riemannian manifold. Using the tensor rank decomposition, we then generalise this principle in order to have a well-defined notion of the topology and geometry for a large class of tensors $P_{abc}$. We provide some examples of the emergence of a topology and measure of both exact and perturbed Riemannian manifolds, and of a purely algebraically-defined space called the semi-local circle.
{"title":"Tensors and Algebras: An Algebraic Spacetime Interpretation for Tensor Models","authors":"Dennis Obster","doi":"10.3842/sigma.2023.076","DOIUrl":"https://doi.org/10.3842/sigma.2023.076","url":null,"abstract":"The quest for a consistent theory for quantum gravity is one of the most challenging problems in theoretical high-energy physics. An often-used approach is to describe the gravitational degrees of freedom by the metric tensor or related variables, and finding a way to quantise this. In the canonical tensor model, the gravitational degrees of freedom are encoded in a tensorial quantity $P_{abc}$, and this quantity is subsequently quantised. This makes the quantisation much more straightforward mathematically, but the interpretation of this tensor as a spacetime is less evident. In this work we take a first step towards fully understanding the relationship to spacetime. By considering $P_{abc}$ as the generator of an algebra of functions, we first describe how we can recover the topology and the measure of a compact Riemannian manifold. Using the tensor rank decomposition, we then generalise this principle in order to have a well-defined notion of the topology and geometry for a large class of tensors $P_{abc}$. We provide some examples of the emergence of a topology and measure of both exact and perturbed Riemannian manifolds, and of a purely algebraically-defined space called the semi-local circle.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135883909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nicolas Crampe, Luc Frappat, Loic Poulain d'Andecy, Eric Ragoucy
We propose a definition by generators and relations of the rank $n-2$ Askey-Wilson algebra $mathfrak{aw}(n)$ for any integer $n$, generalising the known presentation for the usual case $n=3$. The generators are indexed by connected subsets of ${1,dots,n}$ and the simple and rather small set of defining relations is directly inspired from the known case of $n=3$. Our first main result is to prove the existence of automorphisms of $mathfrak{aw}(n)$ satisfying the relations of the braid group on $n+1$ strands. We also show the existence of coproduct maps relating the algebras for different values of $n$. An immediate consequence of our approach is that the Askey-Wilson algebra defined here surjects onto the algebra generated by the intermediate Casimir elements in the $n$-fold tensor product of the quantum group ${rm U}_q(mathfrak{sl}_2)$ or, equivalently, onto the Kauffman bracket skein algebra of the $(n+1)$-punctured sphere. We also obtain a family of central elements of the Askey-Wilson algebras which are shown, as a direct by-product of our construction, to be sent to $0$ in the realisation in the $n$-fold tensor product of ${rm U}_q(mathfrak{sl}_2)$, thereby producing a large number of relations for the algebra generated by the intermediate Casimir elements.
对于任意整数$n$，我们提出了秩$n-2$ Askey-Wilson代数$mathfrak{aw}(n)$的一个定义，推广了通常情况$n=3$的已知表示。生成器由${1，dots,n}$的连通子集索引，简单而相当小的定义关系集直接来自于已知的$n=3$的情况。我们的第一个主要结果是证明了$mathfrak{aw}(n)$的自同构的存在性，满足$n+1$链上编织群的关系。我们还证明了不同n值下代数的余积映射的存在性。我们的方法的一个直接结果是，这里定义的Askey-Wilson代数被投射到由量子群${rm U}_q(mathfrak{sl}_2)$ n -fold张量积$n -fold张量积中的中间卡西米尔元素所产生的代数上，或者等价地，投射到$(n+1)$-穿球的Kauffman括号串代数上。我们还得到了Askey-Wilson代数的一组中心元素，作为我们构造的直接副产品，它们在${rm U}_q(mathfrak{sl}_2)$的$n$次张量积的实现中被送至$0$，从而产生了由中间卡西米尔元素生成的代数的大量关系。
{"title":"The Higher-Rank Askey-Wilson Algebra and Its Braid Group Automorphisms","authors":"Nicolas Crampe, Luc Frappat, Loic Poulain d'Andecy, Eric Ragoucy","doi":"10.3842/sigma.2023.077","DOIUrl":"https://doi.org/10.3842/sigma.2023.077","url":null,"abstract":"We propose a definition by generators and relations of the rank $n-2$ Askey-Wilson algebra $mathfrak{aw}(n)$ for any integer $n$, generalising the known presentation for the usual case $n=3$. The generators are indexed by connected subsets of ${1,dots,n}$ and the simple and rather small set of defining relations is directly inspired from the known case of $n=3$. Our first main result is to prove the existence of automorphisms of $mathfrak{aw}(n)$ satisfying the relations of the braid group on $n+1$ strands. We also show the existence of coproduct maps relating the algebras for different values of $n$. An immediate consequence of our approach is that the Askey-Wilson algebra defined here surjects onto the algebra generated by the intermediate Casimir elements in the $n$-fold tensor product of the quantum group ${rm U}_q(mathfrak{sl}_2)$ or, equivalently, onto the Kauffman bracket skein algebra of the $(n+1)$-punctured sphere. We also obtain a family of central elements of the Askey-Wilson algebras which are shown, as a direct by-product of our construction, to be sent to $0$ in the realisation in the $n$-fold tensor product of ${rm U}_q(mathfrak{sl}_2)$, thereby producing a large number of relations for the algebra generated by the intermediate Casimir elements.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove and generalize several recent conjectures of Z.-W. Sun surrounding binomial coefficients and harmonic numbers. We show that Sun's series and their analogs can be represented as cyclotomic multiple zeta values of levels $Nin{4,8,12,16,24}$, namely Goncharov's multiple polylogarithms evaluated at $N$-th roots of unity.
{"title":"Sun's Series via Cyclotomic Multiple Zeta Values","authors":"Yajun Zhou","doi":"10.3842/sigma.2023.074","DOIUrl":"https://doi.org/10.3842/sigma.2023.074","url":null,"abstract":"We prove and generalize several recent conjectures of Z.-W. Sun surrounding binomial coefficients and harmonic numbers. We show that Sun's series and their analogs can be represented as cyclotomic multiple zeta values of levels $Nin{4,8,12,16,24}$, namely Goncharov's multiple polylogarithms evaluated at $N$-th roots of unity.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135969967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We construct a separable Frobenius monoidal functor from $mathcal{Z}big(mathsf{Vect}_H^{omega|_H}big)$ to $mathcal{Z}big(mathsf{Vect}_G^omegabig)$ for any subgroup $H$ of $G$ which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in $mathcal{Z}big(mathsf{Vect}_G^omegabig)$, recovering the classification of étale algebras in these categories by Davydov-Simmons [J. Algebra 471 (2017), 149-175, arXiv:1603.04650] and generalizing their classification to algebraically closed fields of arbitrary characteristic. Categories of local modules over such algebras are modular tensor categories by results of Kirillov-Ostrik [Adv. Math. 171 (2002), 183-227, arXiv:math.QA/0101219] in the semisimple case and Laugwitz-Walton [Comm. Math. Phys., to appear, arXiv:2202.08644] in the general case.
{"title":"Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras","authors":"Samuel Hannah, Robert Laugwitz, Ana Ros Camacho","doi":"10.3842/sigma.2023.075","DOIUrl":"https://doi.org/10.3842/sigma.2023.075","url":null,"abstract":"We construct a separable Frobenius monoidal functor from $mathcal{Z}big(mathsf{Vect}_H^{omega|_H}big)$ to $mathcal{Z}big(mathsf{Vect}_G^omegabig)$ for any subgroup $H$ of $G$ which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in $mathcal{Z}big(mathsf{Vect}_G^omegabig)$, recovering the classification of étale algebras in these categories by Davydov-Simmons [J. Algebra 471 (2017), 149-175, arXiv:1603.04650] and generalizing their classification to algebraically closed fields of arbitrary characteristic. Categories of local modules over such algebras are modular tensor categories by results of Kirillov-Ostrik [Adv. Math. 171 (2002), 183-227, arXiv:math.QA/0101219] in the semisimple case and Laugwitz-Walton [Comm. Math. Phys., to appear, arXiv:2202.08644] in the general case.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135970123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) $B$. Rigid body quantization, in which one quantizes motion on the spin-isospin orbit of just one minimum, is thus an ill-justified approximation. Instead, one should identify a (finite-dimensional) moduli space of configurations containing all local minima (for a given $B$) as well as fields interpolating smoothly between them. This paper proposes a systematic computational scheme for generating such a moduli space: one constructs an energy minimizing path between each pair of local minima, then defines the moduli space to be the union of spin-isospin orbits of points on the union of these curves, a principal bundle over a graph. The energy minimizing curves may be constructed in practice using the nudged elastic band method, a standard tool in mathematical chemistry for analyzing reaction paths and computing activation energies. To illustrate, we apply this scheme to the lightly bound Skyrme model in the point particle approximation, constructing the graphs for $5leq Bleq 10$. We go on to complete the quantization for $B=7$, in which the graph has two vertices and a single edge. The low-lying quantum states with isospin $1/2$ do not strongly localize around either of the local energy minima (the vertices). Their energies rise monotonically with spin, conflicting with experimental data for Lithium-7.
{"title":"Nudged Elastic Bands and Lightly Bound Skyrmions","authors":"James Martin Speight, Thomas Winyard","doi":"10.3842/sigma.2023.073","DOIUrl":"https://doi.org/10.3842/sigma.2023.073","url":null,"abstract":"It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) $B$. Rigid body quantization, in which one quantizes motion on the spin-isospin orbit of just one minimum, is thus an ill-justified approximation. Instead, one should identify a (finite-dimensional) moduli space of configurations containing all local minima (for a given $B$) as well as fields interpolating smoothly between them. This paper proposes a systematic computational scheme for generating such a moduli space: one constructs an energy minimizing path between each pair of local minima, then defines the moduli space to be the union of spin-isospin orbits of points on the union of these curves, a principal bundle over a graph. The energy minimizing curves may be constructed in practice using the nudged elastic band method, a standard tool in mathematical chemistry for analyzing reaction paths and computing activation energies. To illustrate, we apply this scheme to the lightly bound Skyrme model in the point particle approximation, constructing the graphs for $5leq Bleq 10$. We go on to complete the quantization for $B=7$, in which the graph has two vertices and a single edge. The low-lying quantum states with isospin $1/2$ do not strongly localize around either of the local energy minima (the vertices). Their energies rise monotonically with spin, conflicting with experimental data for Lithium-7.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"198 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136208632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is known that extreme characters of several inductive limits of compact groups exhibit multiplicativity in a certain sense. In the paper, we formulate such multiplicativity for inductive limit quantum groups and provide explicit examples of multiplicative characters in the case of quantum unitary groups. Furthermore, we show a Gaussian fluctuation limit theorem using this concept of multiplicativity.
{"title":"Multiplicative Characters and Gaussian Fluctuation Limits","authors":"Ryosuke Sato","doi":"10.3842/sigma.2023.072","DOIUrl":"https://doi.org/10.3842/sigma.2023.072","url":null,"abstract":"It is known that extreme characters of several inductive limits of compact groups exhibit multiplicativity in a certain sense. In the paper, we formulate such multiplicativity for inductive limit quantum groups and provide explicit examples of multiplicative characters in the case of quantum unitary groups. Furthermore, we show a Gaussian fluctuation limit theorem using this concept of multiplicativity.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135739054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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