Pub Date : 2025-04-28DOI: 10.1016/j.indag.2025.04.004
Dominik Brennecken
We introduce a Cherednik kernel and a hypergeometric function for integral root systems and prove their relation to spherical functions associated with Riemannian symmetric spaces of reductive Lie groups. Furthermore, we characterize the spectral parameters for which the Cherednik kernel is a bounded function. In the case of a crystallographic root system, this characterization was proven by Narayanan, Pasquale and Pusti for the hypergeometric function. This result generalizes the Helgason–Johnson theorem from 1969, which characterizes the bounded spherical functions of a Riemannian symmetric space. The characterization for the Cherednik kernel is based on recurrence relations for the associated Cherednik operators under the dual affine Weyl group going back to Sahi. These recurrence relations are also used to prove a limit transition between the Cherednik kernel of type and of type , which generalizes an already known result for the associated hypergeometric functions by Rösler, Koornwinder, and Voit.
{"title":"Boundedness of the Cherednik kernel and its limit transition from type BC to type A","authors":"Dominik Brennecken","doi":"10.1016/j.indag.2025.04.004","DOIUrl":"10.1016/j.indag.2025.04.004","url":null,"abstract":"<div><div>We introduce a Cherednik kernel and a hypergeometric function for integral root systems and prove their relation to spherical functions associated with Riemannian symmetric spaces of reductive Lie groups. Furthermore, we characterize the spectral parameters for which the Cherednik kernel is a bounded function. In the case of a crystallographic root system, this characterization was proven by Narayanan, Pasquale and Pusti for the hypergeometric function. This result generalizes the Helgason–Johnson theorem from 1969, which characterizes the bounded spherical functions of a Riemannian symmetric space. The characterization for the Cherednik kernel is based on recurrence relations for the associated Cherednik operators under the dual affine Weyl group going back to Sahi. These recurrence relations are also used to prove a limit transition between the Cherednik kernel of type <span><math><mi>A</mi></math></span> and of type <span><math><mi>B</mi></math></span>, which generalizes an already known result for the associated hypergeometric functions by Rösler, Koornwinder, and Voit.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 6","pages":"Pages 1717-1744"},"PeriodicalIF":0.8,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145374395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-15DOI: 10.1016/j.indag.2025.04.002
Kalyan Banerjee
In this short note we prove that an involution on certain examples of surfaces of general type with , acts as identity on the Chow group of zero cycles of the relevant surface. In particular we consider examples of such surfaces when the quotient is an Enriques surface and show that the Bloch conjecture holds for such surfaces.
{"title":"Bloch’s conjecture on certain surfaces of general type with pg=0 and with an involution: The Enriques case","authors":"Kalyan Banerjee","doi":"10.1016/j.indag.2025.04.002","DOIUrl":"10.1016/j.indag.2025.04.002","url":null,"abstract":"<div><div>In this short note we prove that an involution on certain examples of surfaces of general type with <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span>, acts as identity on the Chow group of zero cycles of the relevant surface. In particular we consider examples of such surfaces when the quotient is an Enriques surface and show that the Bloch conjecture holds for such surfaces.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1329-1335"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-11DOI: 10.1016/j.indag.2025.04.001
Mieke Wessel
We give a new graph-theoretic proof of a theorem of Cobham which says that the support of an automatic sequence is either sparse, that is, grows polylogarithmically, or grows at least like for some . The proof uses the notions of tied vertices and cycle arborescences. With the ideas of the proof we can also give a new interpretation of the rank of a sparse sequence as the height of its cycle arborescence. In the non-sparse case we are able to show that the support has asymptotic behavior of the form , where turns out to be the logarithm of an integer root of a Perron number.
{"title":"A graph-theoretic proof of Cobham’s Dichotomy for automatic sequences","authors":"Mieke Wessel","doi":"10.1016/j.indag.2025.04.001","DOIUrl":"10.1016/j.indag.2025.04.001","url":null,"abstract":"<div><div>We give a new graph-theoretic proof of a theorem of Cobham which says that the support of an automatic sequence is either sparse, that is, grows polylogarithmically, or grows at least like <span><math><msup><mrow><mi>N</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span> for some <span><math><mrow><mi>α</mi><mo>></mo><mn>0</mn></mrow></math></span>. The proof uses the notions of tied vertices and cycle arborescences. With the ideas of the proof we can also give a new interpretation of the rank of a sparse sequence as the height of its cycle arborescence. In the non-sparse case we are able to show that the support has asymptotic behavior of the form <span><math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mi>B</mi></mrow></msup><mo>log</mo><msup><mrow><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>, where <span><math><mi>B</mi></math></span> turns out to be the logarithm of an integer root of a Perron number.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1310-1328"},"PeriodicalIF":0.8,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-11DOI: 10.1016/j.indag.2025.03.011
Tanushree Shah
We classify tight contact structures with zero Giroux torsion on some Seifert-fibered manifolds with four exceptional fibers. We get the lower bound by constructing contact structures using Legendrian surgery. We use convex surface theory to obtain the upper bound.
{"title":"Classification of tight contact structures on some Seifert fibered manifolds","authors":"Tanushree Shah","doi":"10.1016/j.indag.2025.03.011","DOIUrl":"10.1016/j.indag.2025.03.011","url":null,"abstract":"<div><div>We classify tight contact structures with zero Giroux torsion on some Seifert-fibered manifolds with four exceptional fibers. We get the lower bound by constructing contact structures using Legendrian surgery. We use convex surface theory to obtain the upper bound.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1288-1309"},"PeriodicalIF":0.8,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-08DOI: 10.1016/j.indag.2025.03.009
Lukas Langen, Margit Rösler
We establish a multiresolution analysis on the space of complex Hermitian matrices which is adapted to invariance under conjugation by the unitary group The orbits under this action are parametrized by the possible ordered spectra of Hermitian matrices, which constitute a closed Weyl chamber of type in . The space of radial, i.e. -invariant -functions on is naturally identified with a certain weighted -space on this chamber.
The scale spaces of our multiresolution analysis are obtained by usual dyadic dilations as well as generalized translations of a scaling function, where the generalized translation is a hypergroup translation which respects the radial geometry. We provide a concise criterion to characterize orthonormal wavelet bases and show that such bases always exist. They provide natural orthonormal bases of the space Furthermore, we show how to obtain radial scaling functions from classical scaling functions on . Finally, generalizations related to the Cartan decompositions for general compact Lie groups are indicated.
{"title":"Multiresolution analysis on spectra of Hermitian matrices","authors":"Lukas Langen, Margit Rösler","doi":"10.1016/j.indag.2025.03.009","DOIUrl":"10.1016/j.indag.2025.03.009","url":null,"abstract":"<div><div>We establish a multiresolution analysis on the space <span><math><mrow><mtext>Herm</mtext><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> of <span><math><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></math></span> complex Hermitian matrices which is adapted to invariance under conjugation by the unitary group <span><math><mrow><mi>U</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>.</mo></mrow></math></span> The orbits under this action are parametrized by the possible ordered spectra of Hermitian matrices, which constitute a closed Weyl chamber of type <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. The space <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mrow><mo>(</mo><mtext>Herm</mtext><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mi>U</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></msup></mrow></math></span> of radial, <em>i.e</em>. <span><math><mrow><mi>U</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span>-invariant <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-functions on <span><math><mrow><mtext>Herm</mtext><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> is naturally identified with a certain weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-space on this chamber.</div><div>The scale spaces of our multiresolution analysis are obtained by usual dyadic dilations as well as generalized translations of a scaling function, where the generalized translation is a hypergroup translation which respects the radial geometry. We provide a concise criterion to characterize orthonormal wavelet bases and show that such bases always exist. They provide natural orthonormal bases of the space <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mrow><mo>(</mo><mtext>Herm</mtext><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mi>U</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></msup><mo>.</mo></mrow></math></span> Furthermore, we show how to obtain radial scaling functions from classical scaling functions on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Finally, generalizations related to the Cartan decompositions for general compact Lie groups are indicated.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 6","pages":"Pages 1671-1694"},"PeriodicalIF":0.8,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145374695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-04DOI: 10.1016/j.indag.2025.03.010
Martin Auer, Michael Voit
After some normalization, the logarithms of the ordered singular values of Brownian motions on with form Weyl-group invariant Heckman–Opdam processes on of type . We use classical elementary formulas for the spherical functions of and the associated Euclidean spaces of Hermitian matrices, and show that in the -case, these processes can be also interpreted as ordered eigenvalues of Brownian motions on with particular drifts. This leads to an explicit description for the free limits for the associated empirical processes for where these limits are independent from the parameter of the Heckman–Opdam processes. In particular we get new formulas for the distributions of the free multiplicative Brownian motion of Biane. We also show how this approach works for the root systems .
{"title":"An explicit formula for free multiplicative Brownian motions via spherical functions","authors":"Martin Auer, Michael Voit","doi":"10.1016/j.indag.2025.03.010","DOIUrl":"10.1016/j.indag.2025.03.010","url":null,"abstract":"<div><div>After some normalization, the logarithms of the ordered singular values of Brownian motions on <span><math><mrow><mi>G</mi><mi>L</mi><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mi>F</mi><mo>=</mo><mi>R</mi><mo>,</mo><mi>ℂ</mi></mrow></math></span> form Weyl-group invariant Heckman–Opdam processes on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> of type <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span>. We use classical elementary formulas for the spherical functions of <span><math><mrow><mi>G</mi><mi>L</mi><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>ℂ</mi><mo>)</mo></mrow><mo>/</mo><mi>S</mi><mi>U</mi><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span> and the associated Euclidean spaces <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>ℂ</mi><mo>)</mo></mrow></mrow></math></span> of Hermitian matrices, and show that in the <span><math><mrow><mi>G</mi><mi>L</mi><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>ℂ</mi><mo>)</mo></mrow></mrow></math></span>-case, these processes can be also interpreted as ordered eigenvalues of Brownian motions on <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>ℂ</mi><mo>)</mo></mrow></mrow></math></span> with particular drifts. This leads to an explicit description for the free limits for the associated empirical processes for <span><math><mrow><mi>N</mi><mo>→</mo><mi>∞</mi></mrow></math></span> where these limits are independent from the parameter <span><math><mi>k</mi></math></span> of the Heckman–Opdam processes. In particular we get new formulas for the distributions of the free multiplicative Brownian motion of Biane. We also show how this approach works for the root systems <span><math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 6","pages":"Pages 1695-1716"},"PeriodicalIF":0.8,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145374394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-01DOI: 10.1016/j.indag.2025.03.007
Eugenio P. Balanzario
We consider the distribution of values of weighted sums of the von Mangoldt arithmetical function. Using a formula for the distribution of values of trigonometric polynomials, we are able to present evidence supporting the claim that these weighted sums follow a distribution with a normal-like behavior.
{"title":"A note on the distribution of clusters and deserts of prime numbers","authors":"Eugenio P. Balanzario","doi":"10.1016/j.indag.2025.03.007","DOIUrl":"10.1016/j.indag.2025.03.007","url":null,"abstract":"<div><div>We consider the distribution of values of weighted sums of the von Mangoldt arithmetical function. Using a formula for the distribution of values of trigonometric polynomials, we are able to present evidence supporting the claim that these weighted sums follow a distribution with a normal-like behavior.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1276-1287"},"PeriodicalIF":0.8,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-26DOI: 10.1016/j.indag.2025.03.005
Piotr Nowakowski
Let be the central Cantor set generated by a sequence . It is known that the difference set has one of three possible forms: a finite union of closed intervals, a Cantor set, or a Cantorval. In the previous paper (Filipczak and Nowakowski, 2023), there was given the sufficient condition for the sequence , which implies that is a Cantorval. In this paper we give different conditions for a sequence , which guarantee the same assertion. We also prove a corollary, which provides infinitely many new examples of Cantorvals.
设C(a)∧[0,1]是由序列a=(an)∈0,1n生成的中心康托集。已知差分集C(a)−C(a)具有三种可能的形式之一：闭区间的有限并、Cantor集或Cantorval集。在之前的论文（Filipczak and Nowakowski, 2023）中，给出了序列a的充分条件，这意味着C(a)−C(a)是Cantorval。本文给出了序列a的不同条件，以保证同一断言。我们还证明了一个推论，该推论提供了无限多的Cantorvals的新例子。
{"title":"Conditions for the difference set of a central Cantor set to be a Cantorval. Part II","authors":"Piotr Nowakowski","doi":"10.1016/j.indag.2025.03.005","DOIUrl":"10.1016/j.indag.2025.03.005","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mo>⊂</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span> be the central Cantor set generated by a sequence <span><math><mrow><mi>a</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mfenced><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span>. It is known that the difference set <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mo>−</mo><mi>C</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow></mrow></math></span> has one of three possible forms: a finite union of closed intervals, a Cantor set, or a Cantorval. In the previous paper (Filipczak and Nowakowski, 2023), there was given the sufficient condition for the sequence <span><math><mi>a</mi></math></span>, which implies that <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mo>−</mo><mi>C</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow></mrow></math></span> is a Cantorval. In this paper we give different conditions for a sequence <span><math><mi>a</mi></math></span>, which guarantee the same assertion. We also prove a corollary, which provides infinitely many new examples of Cantorvals.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1223-1244"},"PeriodicalIF":0.8,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-26DOI: 10.1016/j.indag.2025.03.004
K. De Commer
We investigate the theory of induction in the setting of doubles of coideal -subalgebras of compact quantum group Hopf -algebras. We then exemplify parts of this theory in the particular case of quantum , and compute the decomposition of the regular representation for quantum into irreducibles.
{"title":"Induction for representations of coideal doubles, with an application to quantum SL(2,R)","authors":"K. De Commer","doi":"10.1016/j.indag.2025.03.004","DOIUrl":"10.1016/j.indag.2025.03.004","url":null,"abstract":"<div><div>We investigate the theory of induction in the setting of doubles of coideal <span><math><mo>∗</mo></math></span>-subalgebras of compact quantum group Hopf <span><math><mo>∗</mo></math></span>-algebras. We then exemplify parts of this theory in the particular case of quantum <span><math><mrow><mi>S</mi><mi>L</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>, and compute the decomposition of the regular representation for quantum <span><math><mrow><mi>S</mi><mi>L</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> into irreducibles.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 6","pages":"Pages 1628-1670"},"PeriodicalIF":0.8,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145374396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-26DOI: 10.1016/j.indag.2025.03.003
Giovanna Carnovale , Nicola Ciccoli , Elena Collacciani
The Drinfeld double of a finite group appears in many different areas of mathematics and physics. We review different instances in which the Drinfeld double of a finite group and its representations play a role, focusing on some of Tom Koornwinder’s research interests: harmonic analysis, Lie algebras, quantum groups, non-commutative geometry, and Verlinde formula for fusion rules.
{"title":"The versatility of the Drinfeld double of a finite group","authors":"Giovanna Carnovale , Nicola Ciccoli , Elena Collacciani","doi":"10.1016/j.indag.2025.03.003","DOIUrl":"10.1016/j.indag.2025.03.003","url":null,"abstract":"<div><div>The Drinfeld double of a finite group appears in many different areas of mathematics and physics<span><span>. We review different instances in which the Drinfeld double of a finite group and its representations play a role, focusing on some of Tom Koornwinder’s research interests: harmonic analysis, Lie algebras, </span>quantum groups, non-commutative geometry, and Verlinde formula for fusion rules.</span></div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 6","pages":"Pages 1600-1627"},"PeriodicalIF":0.8,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145374686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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