Super Vust theorem and Schur-Sergeev duality for principal finite W-superalgebras

Changjie Cheng; Bin Shu; Yang Zeng

doi:10.1016/j.jalgebra.2025.02.017

Super Vust theorem and Schur-Sergeev duality for principal finite W-superalgebras

Changjie Cheng
, Bin Shu
, Yang Zeng

School of Mathematical Sciences

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

Abstract

Considering the general linear Lie superalgebra gl(m|n)=gl(m|n)_0¯¯⊕gl(m|n)_1¯¯ over C, we first formulate a super version of Vust theorem associated with a principal nilpotent element e∈gl(m|n)_0¯¯. As an application of this theorem, we then obtain a Schur-Sergeev duality for principal finite W-superalgebras which is partially a super version of Brundan-Kleshchev's higher level Schur-Weyl duality established in [7].

Original language	English
Pages (from-to)	138-187
Number of pages	50
Journal	Journal of Algebra
Volume	673
DOIs	https://doi.org/10.1016/j.jalgebra.2025.02.017
State	Published - 1 Jul 2025

Keywords

Degenerate cyclotomic Hecke algebras
Double centralizer property
Finite W-superalgebras
Kazhdan-filtration
Principal (regular) nilpotent orbits
Schur-Sergeev duality
Schur-Weyl duality

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10.1016/j.jalgebra.2025.02.017

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title = "Super Vust theorem and Schur-Sergeev duality for principal finite W-superalgebras",

abstract = "Considering the general linear Lie superalgebra gl(m|n)=gl(m|n)0¯¯⊕gl(m|n)1¯¯ over C, we first formulate a super version of Vust theorem associated with a principal nilpotent element e∈gl(m|n)0¯¯. As an application of this theorem, we then obtain a Schur-Sergeev duality for principal finite W-superalgebras which is partially a super version of Brundan-Kleshchev's higher level Schur-Weyl duality established in [7].",

keywords = "Degenerate cyclotomic Hecke algebras, Double centralizer property, Finite W-superalgebras, Kazhdan-filtration, Principal (regular) nilpotent orbits, Schur-Sergeev duality, Schur-Weyl duality",

author = "Changjie Cheng and Bin Shu and Yang Zeng",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Inc.",

year = "2025",

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day = "1",

doi = "10.1016/j.jalgebra.2025.02.017",

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T1 - Super Vust theorem and Schur-Sergeev duality for principal finite W-superalgebras

AU - Cheng, Changjie

AU - Shu, Bin

AU - Zeng, Yang

PY - 2025/7/1

Y1 - 2025/7/1

N2 - Considering the general linear Lie superalgebra gl(m|n)=gl(m|n)0¯¯⊕gl(m|n)1¯¯ over C, we first formulate a super version of Vust theorem associated with a principal nilpotent element e∈gl(m|n)0¯¯. As an application of this theorem, we then obtain a Schur-Sergeev duality for principal finite W-superalgebras which is partially a super version of Brundan-Kleshchev's higher level Schur-Weyl duality established in [7].

AB - Considering the general linear Lie superalgebra gl(m|n)=gl(m|n)0¯¯⊕gl(m|n)1¯¯ over C, we first formulate a super version of Vust theorem associated with a principal nilpotent element e∈gl(m|n)0¯¯. As an application of this theorem, we then obtain a Schur-Sergeev duality for principal finite W-superalgebras which is partially a super version of Brundan-Kleshchev's higher level Schur-Weyl duality established in [7].

KW - Degenerate cyclotomic Hecke algebras

KW - Double centralizer property

KW - Finite W-superalgebras

KW - Kazhdan-filtration

KW - Principal (regular) nilpotent orbits

KW - Schur-Sergeev duality

KW - Schur-Weyl duality

UR - https://www.scopus.com/pages/publications/86000787866

U2 - 10.1016/j.jalgebra.2025.02.017

DO - 10.1016/j.jalgebra.2025.02.017

M3 - 文章

AN - SCOPUS:86000787866

SN - 0021-8693

VL - 673

SP - 138

EP - 187

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Super Vust theorem and Schur-Sergeev duality for principal finite W-superalgebras

Abstract

Keywords

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