Pub Date : 2020-05-03DOI: 10.1215/21562261-10428418
Sanjay Amrutiya, U. Dubey
We give functorial moduli construction of pure parabolic sheaves, in the sense of Alvarez-Consul and A. King, using the moduli of filtered Kronecker modules which we introduced in our earlier work. We also use a version of S. G. Langton's result due to K. Yokogawa to deduce the projectivity of moduli of parabolic sheaves. As an application of functorial moduli construction, we can get the morphisms at the level of moduli stacks.
{"title":"Moduli of parabolic sheaves and filtered Kronecker modules","authors":"Sanjay Amrutiya, U. Dubey","doi":"10.1215/21562261-10428418","DOIUrl":"https://doi.org/10.1215/21562261-10428418","url":null,"abstract":"We give functorial moduli construction of pure parabolic sheaves, in the sense of Alvarez-Consul and A. King, using the moduli of filtered Kronecker modules which we introduced in our earlier work. We also use a version of S. G. Langton's result due to K. Yokogawa to deduce the projectivity of moduli of parabolic sheaves. As an application of functorial moduli construction, we can get the morphisms at the level of moduli stacks.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47041431","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 : 2020-04-04DOI: 10.1215/21562261-2022-0016
Leon Barth, Deniz Kus
We determine the graded decompositions of fusion products of finite-dimensional irreducible representations for simple Lie algebras of rank two. Moreover, we give generators and relations for these representations and obtain as a consequence that the Schur positivity conjecture holds in this case. The graded Littlewood-Richardson coefficients in the decomposition are parametrized by lattice points in convex polytopes and an explicit hyperplane description is given in the various types.
{"title":"Graded decompositions of fusion products in rank 2","authors":"Leon Barth, Deniz Kus","doi":"10.1215/21562261-2022-0016","DOIUrl":"https://doi.org/10.1215/21562261-2022-0016","url":null,"abstract":"We determine the graded decompositions of fusion products of finite-dimensional irreducible representations for simple Lie algebras of rank two. Moreover, we give generators and relations for these representations and obtain as a consequence that the Schur positivity conjecture holds in this case. The graded Littlewood-Richardson coefficients in the decomposition are parametrized by lattice points in convex polytopes and an explicit hyperplane description is given in the various types.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66025447","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 : 2020-04-01DOI: 10.1215/21562261-2019-0035
V. Burenkov, E. Liflyand
{"title":"Hausdorff operators on Morrey-type spaces","authors":"V. Burenkov, E. Liflyand","doi":"10.1215/21562261-2019-0035","DOIUrl":"https://doi.org/10.1215/21562261-2019-0035","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"60 1","pages":"93-106"},"PeriodicalIF":0.6,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-2019-0035","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43416951","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 : 2020-04-01DOI: 10.1215/21562261-2019-0037
Helena Cobo, M. Soto, J. Tornero
{"title":"Blurred combinatorics in resolution of singularities: (A little) Beyond the characteristic polytope","authors":"Helena Cobo, M. Soto, J. Tornero","doi":"10.1215/21562261-2019-0037","DOIUrl":"https://doi.org/10.1215/21562261-2019-0037","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"60 1","pages":"269-289"},"PeriodicalIF":0.6,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48530741","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 : 2020-03-24DOI: 10.1215/21562261-2022-0033
N. Addington, Franco Giovenzana
For the irreducible holomorphic symplectic eightfold Z associated to a cubic fourfold Y not containing a plane, we show that a natural Abel-Jacobi map from H^4_prim(Y) to H^2_prim(Z) is a Hodge isometry. We describe the full H^2(Z) in terms of the Mukai lattice of the K3 category A of Y. We give numerical conditions for Z to be birational to a moduli space of sheaves on a K3 surface or to Hilb^4(K3). We propose a conjecture on how to use Z to produce equivalences from A to the derived category of a K3 surface.
{"title":"On the period of Lehn, Lehn, Sorger, and van Straten’s symplectic eightfold","authors":"N. Addington, Franco Giovenzana","doi":"10.1215/21562261-2022-0033","DOIUrl":"https://doi.org/10.1215/21562261-2022-0033","url":null,"abstract":"For the irreducible holomorphic symplectic eightfold Z associated to a cubic fourfold Y not containing a plane, we show that a natural Abel-Jacobi map from H^4_prim(Y) to H^2_prim(Z) is a Hodge isometry. We describe the full H^2(Z) in terms of the Mukai lattice of the K3 category A of Y. We give numerical conditions for Z to be birational to a moduli space of sheaves on a K3 surface or to Hilb^4(K3). We propose a conjecture on how to use Z to produce equivalences from A to the derived category of a K3 surface.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47754304","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 : 2020-03-05DOI: 10.1215/21562261-2021-0008
K. Cieliebak, E. Volkov
We introduce eight versions of cyclic homology of a mixed complex and study their properties. In particular, we determine their behaviour with respect to Chen iterated integrals.
{"title":"Eight flavors of cyclic homology","authors":"K. Cieliebak, E. Volkov","doi":"10.1215/21562261-2021-0008","DOIUrl":"https://doi.org/10.1215/21562261-2021-0008","url":null,"abstract":"We introduce eight versions of cyclic homology of a mixed complex and study their properties. In particular, we determine their behaviour with respect to Chen iterated integrals.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46703235","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 : 2020-02-25DOI: 10.1215/21562261-2022-0038
Umut Varolgunes
In this paper, we confirm a conjecture of Orlik-Randell from 1977 on the Seifert form of chain type invertible singularities. We use Lefschetz bifibration techniques as developed by Seidel (inspired by Arnold and Donaldson) and take advantage of the symmetries at hand. We believe that our method will be useful in understanding the homological/categorical version of Berglundt-Hubsch mirror conjecture for invertible singularities.
{"title":"Seifert form of chain-type invertible singularities","authors":"Umut Varolgunes","doi":"10.1215/21562261-2022-0038","DOIUrl":"https://doi.org/10.1215/21562261-2022-0038","url":null,"abstract":"In this paper, we confirm a conjecture of Orlik-Randell from 1977 on the Seifert form of chain type invertible singularities. We use Lefschetz bifibration techniques as developed by Seidel (inspired by Arnold and Donaldson) and take advantage of the symmetries at hand. We believe that our method will be useful in understanding the homological/categorical version of Berglundt-Hubsch mirror conjecture for invertible singularities.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44917165","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 : 2020-01-29DOI: 10.1215/21562261-2022-0041
Takaaki Shimura, Toshiro Watanabe
We characterize the subexponential densities on $(0,infty)$ for compound Poisson distributions on $[0,infty)$ with absolutely continuous Levy measures. As a corollary, we show that the class of all subexponential probability density functions on $mathbb R_+$ is closed under generalized convolution roots of compound Poisson sums. Moreover, we give an application to the subexponential density on $(0,infty)$ for the distribution of the supremum of a random walk.
{"title":"Subexponential densities of compound Poisson sums and the supremum of a random walk","authors":"Takaaki Shimura, Toshiro Watanabe","doi":"10.1215/21562261-2022-0041","DOIUrl":"https://doi.org/10.1215/21562261-2022-0041","url":null,"abstract":"We characterize the subexponential densities on $(0,infty)$ for compound Poisson distributions on $[0,infty)$ with absolutely continuous Levy measures. As a corollary, we show that the class of all subexponential probability density functions on $mathbb R_+$ is closed under generalized convolution roots of compound Poisson sums. Moreover, we give an application to the subexponential density on $(0,infty)$ for the distribution of the supremum of a random walk.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41663824","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 : 2020-01-20DOI: 10.1215/21562261-2023-0001
B. Pei, Y. Inahama, Yong Xu
We focus on fast-slow systems involving both fractional Brownian motion (fBm) and standard Brownian motion (Bm). The integral with respect to Bm is the standard Ito integral, and the integral with respect to fBm is the generalised Riemann-Stieltjes integral using the tools of fractional calculus. An averaging principle in which the fast-varying diffusion process of the fast-slow systems acts as a noise to be averaged out in the limit is established. It is shown that the slow process has a limit in the mean square sense, which is characterized by the solution of stochastic differential equations driven by fBm whose coefficients are averaged with respect to the stationary measure of the fast-varying diffusion. The implication is that one can ignore the complex original systems and concentrate on the averaged systems instead. This averaging principle paves the way for reduction of computational complexity.
{"title":"Averaging principles for mixed fast-slow systems driven by fractional Brownian motion","authors":"B. Pei, Y. Inahama, Yong Xu","doi":"10.1215/21562261-2023-0001","DOIUrl":"https://doi.org/10.1215/21562261-2023-0001","url":null,"abstract":"We focus on fast-slow systems involving both fractional Brownian motion (fBm) and standard Brownian motion (Bm). The integral with respect to Bm is the standard Ito integral, and the integral with respect to fBm is the generalised Riemann-Stieltjes integral using the tools of fractional calculus. An averaging principle in which the fast-varying diffusion process of the fast-slow systems acts as a noise to be averaged out in the limit is established. It is shown that the slow process has a limit in the mean square sense, which is characterized by the solution of stochastic differential equations driven by fBm whose coefficients are averaged with respect to the stationary measure of the fast-varying diffusion. The implication is that one can ignore the complex original systems and concentrate on the averaged systems instead. This averaging principle paves the way for reduction of computational complexity.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43105350","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 : 2020-01-12DOI: 10.1215/21562261-2021-0006
H. Nakajima
We prove the conjecture by Gyenge, Nemethi and Szendrői in arXiv:1512.06844, arXiv:1512.06848 giving a formula of the generating function of Euler numbers of Hilbert schemes of points $operatorname{Hilb}^n(mathbb C^2/Gamma)$ on a simple singularity $mathbb C^2/Gamma$, where $Gamma$ is a finite subgroup of $mathrm{SL}(2)$. We deduce it from the claim that quantum dimensions of standard modules for the quantum affine algebra associated with $Gamma$ at $zeta = exp(frac{2pi i}{2(h^vee+1)})$ are always $1$, which is a special case of a conjecture by Kuniba [Kun93]. Here $h^vee$ is the dual Coxeter number. We also prove the claim, which was not known for $E_7$, $E_8$ before.
我们证明了Gyenge，Nemethi和Szendrõi在arXiv:1512066844，arXiv:5152066848中的猜想，给出了点$operatorname{Hilb}^n（mathbb C^2/Gamma）$的Hilbert格式的Euler数在一个简单奇点$mathbb C ^2/Gamma$上的生成函数公式，其中$Gamma$是$mathrm｛SL｝（2）$的有限子群。我们从与$Gamma$相关的量子仿射代数的标准模在$zeta=exp（frac｛2pi i｝｛2（h^vee+1）｝）$处的量子维数总是$1$的声明中推导出，这是Kuniba猜想的一个特例[Kun93]。这里$h^vee$是双Coxeter数。我们还证明了以前$E_7$、$E_8$不为人所知的索赔。
{"title":"Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras","authors":"H. Nakajima","doi":"10.1215/21562261-2021-0006","DOIUrl":"https://doi.org/10.1215/21562261-2021-0006","url":null,"abstract":"We prove the conjecture by Gyenge, Nemethi and Szendrői in arXiv:1512.06844, arXiv:1512.06848 giving a formula of the generating function of Euler numbers of Hilbert schemes of points $operatorname{Hilb}^n(mathbb C^2/Gamma)$ on a simple singularity $mathbb C^2/Gamma$, where $Gamma$ is a finite subgroup of $mathrm{SL}(2)$. We deduce it from the claim that quantum dimensions of standard modules for the quantum affine algebra associated with $Gamma$ at $zeta = exp(frac{2pi i}{2(h^vee+1)})$ are always $1$, which is a special case of a conjecture by Kuniba [Kun93]. Here $h^vee$ is the dual Coxeter number. We also prove the claim, which was not known for $E_7$, $E_8$ before.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42371611","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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