Semisimplicity of the DS functor for the orthosymplectic Lie superalgebra

M. Gorelik; Th Heidersdorf

doi:10.1016/j.aim.2021.108012

Semisimplicity of the DS functor for the orthosymplectic Lie superalgebra

M. Gorelik, Th Heidersdorf

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the Duflo-Serganova functor DS_x attached to an odd nilpotent element x of osp(m|2n) is semisimple, i.e. sends a semisimple representation M of osp(m|2n) to a semisimple representation of osp(m−2k|2n−2k) where k is the rank of x. We prove a closed formula for DS_x(L(λ)) in terms of the arc diagram attached to λ.

Original language	English
Article number	108012
Number of pages	51
Journal	Advances in Mathematics
Volume	394
DOIs	https://doi.org/10.1016/j.aim.2021.108012
State	Published - 22 Jan 2022

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.aim.2021.108012

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title = "Semisimplicity of the DS functor for the orthosymplectic Lie superalgebra",

abstract = "We prove that the Duflo-Serganova functor DSx attached to an odd nilpotent element x of osp(m|2n) is semisimple, i.e. sends a semisimple representation M of osp(m|2n) to a semisimple representation of osp(m−2k|2n−2k) where k is the rank of x. We prove a closed formula for DSx(L(λ)) in terms of the arc diagram attached to λ.",

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AU - Heidersdorf, Th

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N2 - We prove that the Duflo-Serganova functor DSx attached to an odd nilpotent element x of osp(m|2n) is semisimple, i.e. sends a semisimple representation M of osp(m|2n) to a semisimple representation of osp(m−2k|2n−2k) where k is the rank of x. We prove a closed formula for DSx(L(λ)) in terms of the arc diagram attached to λ.

AB - We prove that the Duflo-Serganova functor DSx attached to an odd nilpotent element x of osp(m|2n) is semisimple, i.e. sends a semisimple representation M of osp(m|2n) to a semisimple representation of osp(m−2k|2n−2k) where k is the rank of x. We prove a closed formula for DSx(L(λ)) in terms of the arc diagram attached to λ.

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DO - 10.1016/j.aim.2021.108012

M3 - مقالة

SN - 0001-8708

VL - 394

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 108012

ER -

Semisimplicity of the DS functor for the orthosymplectic Lie superalgebra

Abstract

All Science Journal Classification (ASJC) codes

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