WEYL MODULES FOR LIE SUPERALGEBRAS

被引：6

作者：

Calixto, Lucas ^{[1
,2
]}

Lemay, Joel ^{[3
]}

Savage, Alistair ^{[3
]}

机构：

[1] UNICAMP IMECC, BR-13083859 Campinas, SP, Brazil

[2] Univ Fed Minas Gerais, Dept Math, Belo Horizonte, MG, Brazil

[3] Univ Ottawa, Dept Math & Stat, Ottawa, ON, Canada

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 147卷 / 08期

基金：

巴西圣保罗研究基金会; 加拿大自然科学与工程研究理事会;

关键词：

Lie superalgebra; basic Lie superalgebra; Weyl module; Kac module; tensor product; ALGEBRAS;

D O I：

10.1090/proc/13146

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define global and local Weyl modules for Lie superalgebras of the form g circle times A, where A is an associative commutative unital C-algebra and g is a basic Lie superalgebra or sl(n, n), n >= 2. Under some mild assumptions, we prove universality, finite-dimensionality, and tensor product decomposition properties for these modules. These properties are analogues of those of Weyl modules in the non-super setting. We also point out some features that are new in the super case.

引用

页码：3191 / 3207

页数：17

共 22 条

[1] [Anonymous], 1978, Lect. Notes Math.
[2] Current algebras and categorified quantum groups
Beliakova, Anna
Habiro, Kazuo
Lauda, Aaron D.
Webster, Ben
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2017, 95 : 248 - 276
[3] Equivariant Map Queer Lie Superalgebras
Calixto, Lucas
Moura, Adriano
Savage, Alistair
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2016, 68 (02): : 258 - 279
[4] Chari V., 2001, Representation Theory, V5, P191, DOI [10.1090/S1088-4165-01-00115-7, DOI 10.1090/S1088-4165-01-00115-7]
[5] Weyl modules for the twisted loop algebras
Chari, Vyjayanthi
Fourier, Ghislain
Senesi, Prasad
[J]. JOURNAL OF ALGEBRA, 2008, 319 (12) : 5016 - 5038
[6] A CATEGORICAL APPROACH TO WEYL MODULES
Chari, Vyjayanthi
Fourier, Ghislain
Khandai, Tanusree
[J]. TRANSFORMATION GROUPS, 2010, 15 (03) : 517 - 549
[7] Cheng S.-J., 2012, GRADUATE STUDIES MAT, V144
[8] BOTT-BOREL-WEIL THEORY AND BERNSTEIN-GEL'FAND-GEL'FAND RECIPROCITY FOR LIE SUPERALGEBRAS
Coulembier, Kevin
[J]. TRANSFORMATION GROUPS, 2016, 21 (03) : 681 - 723
[9] Eswara Rao S., 2004, Contemp. Math., V343, P243
[10] Multi-dimensional Weyl modules and symmetric functions
Feigin, B
Loktev, S
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 251 (03) : 427 - 445

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