WEYL MODULES FOR LIE SUPERALGEBRAS

被引：7

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 [J].

Beliakova, Anna ;

Habiro, Kazuo ;

Lauda, Aaron D. ;

Webster, Ben .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2017, 95 :248-276

[3] Equivariant Map Queer Lie Superalgebras [J].

Calixto, Lucas ;

Moura, Adriano ;

Savage, Alistair .

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 [J].

Chari, Vyjayanthi ;

Fourier, Ghislain ;

Senesi, Prasad .

JOURNAL OF ALGEBRA, 2008, 319 (12) :5016-5038

[6] A CATEGORICAL APPROACH TO WEYL MODULES [J].

Chari, Vyjayanthi ;

Fourier, Ghislain ;

Khandai, Tanusree .

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 [J].

Coulembier, Kevin .

TRANSFORMATION GROUPS, 2016, 21 (03) :681-723

[9]

Eswara Rao S., 2004, Contemp. Math., V343, P243

[10] Multi-dimensional Weyl modules and symmetric functions [J].

Feigin, B ;

Loktev, S .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 251 (03) :427-445

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