arXiv - MATH - Representation Theory最新文献_第7页

On Hecke algebras and $Z$-graded twisting, Shuffling and Zuckerman functors 论赫克代数和 $Z$ 级扭转、舒夫林和祖克曼函数

arXiv - MATH - Representation Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03379

Ming Fang, Jun Hu, Yujiao Sun

引用次数: 0

Building blocks for $W$-algebras of classical types 经典类型 $W$ 算法的构件

arXiv - MATH - Representation Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03465

Thomas Creutzig, Vladimir Kovalchuk, Andrew R. Linshaw

{"title":"Building blocks for $W$-algebras of classical types","authors":"Thomas Creutzig, Vladimir Kovalchuk, Andrew R. Linshaw","doi":"arxiv-2409.03465","DOIUrl":"https://doi.org/arxiv-2409.03465","url":null,"abstract":"The universal $2$-parameter vertex algebra $W_{infty}$ of type\u0000$W(2,3,4,dots)$ serves as a classifying object for vertex algebras of type\u0000$W(2,3,dots,N)$ for some $N$ in the sense that under mild hypothesis, all such\u0000vertex algebras arise as quotients of $W_{infty}$. There is an $mathbb{N}\u0000times mathbb{N}$ family of such $1$-parameter vertex algebras known as\u0000$Y$-algebras. They were introduced by Gaiotto and Rapv{c}'ak and are expected\u0000to be the building blocks for all $W$-algebras in type $A$, i.e., every\u0000$W$-(super) algebra in type $A$ is an extension of a tensor product of finitely\u0000many $Y$-algebras. Similarly, the orthosymplectic $Y$-algebras are\u0000$1$-parameter quotients of a universal $2$-parameter vertex algebra\u0000$W^{text{ev}}_{infty}$ of type $W(2,4,6,dots)$, which is a classifying\u0000object for vertex algebras of type $W(2,4,dots, 2N)$ for some $N$. Unlike type\u0000$A$, these algebras are not all the building blocks for $W$-algebras of types\u0000$B$, $C$, and $D$. In this paper, we construct a new universal $2$-parameter\u0000vertex algebra of type $W(1^3, 2, 3^3, 4, 5^3,6,dots)$ which we denote by\u0000$W^{mathfrak{sp}}_{infty}$ since it contains a copy of the affine vertex\u0000algebra $V^k(mathfrak{sp}_2)$. We identify $8$ infinite families of\u0000$1$-parameter quotients of $W^{mathfrak{sp}}_{infty}$ which are analogues of\u0000the $Y$-algebras. We regard $W^{mathfrak{sp}}_{infty}$ as a fundamental\u0000object on equal footing with $W_{infty}$ and $W^{text{ev}}_{infty}$, and we\u0000give some heuristic reasons for why we expect the $1$-parameter quotients of\u0000these three objects to be the building blocks for all $W$-algebras of classical\u0000types. Finally, we prove that $W^{mathfrak{sp}}_{infty}$ has many quotients\u0000which are strongly rational. This yields new examples of strongly rational\u0000$W$-superalgebras.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Whittaker modules for a subalgebra of N=2 superconformal algebra N=2 超共形代数子代数的惠特克模块

arXiv - MATH - Representation Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03159

Naihuan Jing, Pengfa Xu, Honglian Zhang

引用次数: 0

Sheaves of AV-modules on quasi-projective varieties 准投影变体上的 AV 模块的卷积

arXiv - MATH - Representation Theory Pub Date : 2024-09-04 DOI: arxiv-2409.02677

Yuly Billig, Emile Bouaziz

引用次数: 0

Representation Rings of Fusion Systems and Brauer Characters 融合系统和布劳尔字符的表示环

arXiv - MATH - Representation Theory Pub Date : 2024-09-04 DOI: arxiv-2409.03007

Thomas Lawrence

引用次数: 0

Derived structures in the Langlands Correspondence 朗兰兹对应中的衍生结构

arXiv - MATH - Representation Theory Pub Date : 2024-09-04 DOI: arxiv-2409.03035

Tony Feng, Michael Harris

引用次数: 0

Spin Multipartitions 旋转多分区

arXiv - MATH - Representation Theory Pub Date : 2024-09-04 DOI: arxiv-2409.02801

Ola Amara-Omari, Mary Schaps

引用次数: 0

Mixed Tensor Products, Capelli Berezinians, and Newton's Formula for $mathfrak{gl}(m|n)$ 混合张量乘积、卡佩里贝雷津尼和 $mathfrak{gl}(m|n)$ 的牛顿公式

arXiv - MATH - Representation Theory Pub Date : 2024-09-04 DOI: arxiv-2409.02422

Sidarth Erat, Arun S. Kannan, Shihan Kanungo

{"title":"Mixed Tensor Products, Capelli Berezinians, and Newton's Formula for $mathfrak{gl}(m|n)$","authors":"Sidarth Erat, Arun S. Kannan, Shihan Kanungo","doi":"arxiv-2409.02422","DOIUrl":"https://doi.org/arxiv-2409.02422","url":null,"abstract":"In this paper, we extend the results of Grantcharov and Robitaille in 2021 on\u0000mixed tensor products and Capelli determinants to the superalgebra setting.\u0000Specifically, we construct a family of superalgebra homomorphisms $varphi_R :\u0000U(mathfrak{gl}(m+1|n)) rightarrow mathcal{D}'(m|n) otimes\u0000U(mathfrak{gl}(m|n))$ for a certain space of differential operators\u0000$mathcal{D}'(m|n)$ indexed by a central element $R$ of $mathcal{D}'(m|n)\u0000otimes U(mathfrak{gl}(m|n))$. We then use this homomorphism to determine the\u0000image of Gelfand generators of the center of $U(mathfrak{gl}(m+1|n))$. We\u0000achieve this by first relating $varphi_R$ to the corresponding Harish-Chandra\u0000homomorphisms and then proving a super-analog of Newton's formula for\u0000$mathfrak{gl}(m)$ relating Capelli generators and Gelfand generators. We also\u0000use the homomorphism $varphi_R$ to obtain representations of\u0000$U(mathfrak{gl}(m+1|n))$ from those of $U(mathfrak{gl}(m|n))$, and find\u0000conditions under which these inflations are simple. Finally, we show that for a\u0000distinguished central element $R_1$ in $mathcal{D}'(m|n)otimes\u0000U(mathfrak{gl}(m|n))$, the kernel of $varphi_{R_1}$ is the ideal of\u0000$U(mathfrak{gl}(m+1|n))$ generated by the first Gelfand invariant $G_1$.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Geometric realizations of representations for $text{PSL}(2, mathbb{F}_p)$ and Galois representations arising from defining ideals of modular curves $text{PSL}(2, mathbb{F}_p)$和由模态曲线定义理想产生的伽罗瓦表示的几何实现

arXiv - MATH - Representation Theory Pub Date : 2024-09-04 DOI: arxiv-2409.02589

Lei Yang

{"title":"Geometric realizations of representations for $text{PSL}(2, mathbb{F}_p)$ and Galois representations arising from defining ideals of modular curves","authors":"Lei Yang","doi":"arxiv-2409.02589","DOIUrl":"https://doi.org/arxiv-2409.02589","url":null,"abstract":"We construct a geometric realization of representations for $text{PSL}(2,\u0000mathbb{F}_p)$ by the defining ideals of rational models $mathcal{L}(X(p))$ of\u0000modular curves $X(p)$ over $mathbb{Q}$. Hence, for the irreducible\u0000representations of $text{PSL}(2, mathbb{F}_p)$, whose geometric realizations\u0000can be formulated in three different scenarios in the framework of Weil's\u0000Rosetta stone: number fields, curves over $mathbb{F}_q$ and Riemann surfaces.\u0000In particular, we show that there exists a correspondence among the defining\u0000ideals of modular curves over $mathbb{Q}$, reducible\u0000$mathbb{Q}(zeta_p)$-rational representations $pi_p: text{PSL}(2,\u0000mathbb{F}_p) rightarrow text{Aut}(mathcal{L}(X(p)))$ of $text{PSL}(2,\u0000mathbb{F}_p)$, and $mathbb{Q}(zeta_p)$-rational Galois representations\u0000$rho_p: text{Gal}(overline{mathbb{Q}}/mathbb{Q}) rightarrow\u0000text{Aut}(mathcal{L}(X(p)))$ as well as their modular and surjective\u0000realization. This leads to a new viewpoint on the last mathematical testament\u0000of Galois by Galois representations arising from the defining ideals of modular\u0000curves, which leads to a connection with Klein's elliptic modular functions. It\u0000is a nonlinear and anabelian counterpart of the global Langlands correspondence\u0000among the $ell$-adic '{e}tale cohomology of modular curves over $mathbb{Q}$,\u0000i.e., Grothendieck motives ($ell$-adic system), automorphic representations of\u0000$text{GL}(2, mathbb{Q})$ and $ell$-adic representations.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"121 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Combinatorial description of Lusztig $q$-weight multiplicity 卢茨蒂格q$权重多重性的组合描述

arXiv - MATH - Representation Theory Pub Date : 2024-09-04 DOI: arxiv-2409.02341

Seung Jin Lee

引用次数: 0