Semisimplicity of the DS functor for the orthosymplectic Lie superalgebra

被引：6

作者：

Gorelik, M. ^{[1
]}

Heidersdorf, Th ^{[2
]}

机构：

[1] Weizmann Inst Sci, Rehovot, Israel

[2] Univ Bonn, Math Inst, Bonn, Germany

来源：

ADVANCES IN MATHEMATICS | 2022年 / 394卷

关键词：

Representations of supergroups; Duflo-Serganova functor; Superdimensions; Orthosymplectic Lie superalgebra; Orthosymplectic supergroup; Symmetric monoidal functor; REPRESENTATION;

D O I：

10.1016/j.aim.2021.108012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the Duflo-Serganova functor DSx attached to an odd nilpotent element x of osp(m vertical bar 2n) is semisimple, i.e. sends a semisimple representation M of osp(m vertical bar 2n) to a semisimple representation of osp(m - 2k vertical bar 2n - 2k) where k is the rank of x. We prove a closed formula for DSx(L(lambda)) in terms of the arc diagram attached to lambda. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：51

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