On the Duflo-Serganova functor for the queer Lie superalgebra

M. Gorelik; A. Sherman

doi:10.1016/j.aim.2024.109552

On the Duflo-Serganova functor for the queer Lie superalgebra

M. Gorelik, A. Sherman

Weizmann Institute of Science, Ben-Gurion University of the Negev

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Abstract

We study the Duflo-Serganova functor DS_x for the queer Lie superalgebra q_n and for all odd x with [x,x] semisimple. For the case when the rank of x is 1 we give a formula for multiplicities in terms of the arc diagram attached to a dominant weight λ. Further, we prove that DS_x(L) is semisimple if L is a simple finite-dimensional module and x is of rank 1 satisfying x²=0.

Original language	English
Article number	109552
Journal	Advances in Mathematics
Volume	441
DOIs	https://doi.org/10.1016/j.aim.2024.109552
State	Published - 1 Apr 2024

Keywords

Duflo-Serganova functor
Queer Lie superalgebra

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.aim.2024.109552License: CC BY

Cite this

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abstract = "We study the Duflo-Serganova functor DSx for the queer Lie superalgebra qn and for all odd x with [x,x] semisimple. For the case when the rank of x is 1 we give a formula for multiplicities in terms of the arc diagram attached to a dominant weight λ. Further, we prove that DSx(L) is semisimple if L is a simple finite-dimensional module and x is of rank 1 satisfying x2=0.",

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N2 - We study the Duflo-Serganova functor DSx for the queer Lie superalgebra qn and for all odd x with [x,x] semisimple. For the case when the rank of x is 1 we give a formula for multiplicities in terms of the arc diagram attached to a dominant weight λ. Further, we prove that DSx(L) is semisimple if L is a simple finite-dimensional module and x is of rank 1 satisfying x2=0.

AB - We study the Duflo-Serganova functor DSx for the queer Lie superalgebra qn and for all odd x with [x,x] semisimple. For the case when the rank of x is 1 we give a formula for multiplicities in terms of the arc diagram attached to a dominant weight λ. Further, we prove that DSx(L) is semisimple if L is a simple finite-dimensional module and x is of rank 1 satisfying x2=0.

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DO - 10.1016/j.aim.2024.109552

M3 - مقالة

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VL - 441

JO - Advances in Mathematics

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On the Duflo-Serganova functor for the queer Lie superalgebra

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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