On Kac–Weisfeiler modules for general and special linear lie superalgebras

Yang Zeng; Bin Shu

doi:10.1007/s11856-016-1338-1

On Kac–Weisfeiler modules for general and special linear lie superalgebras

Yang Zeng^*, Bin Shu

^*Corresponding author for this work

School of Mathematical Sciences

Nanjing Audit University

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

8 Scopus citations

Abstract

Let g:= gl_m|_n be a general linear Lie superalgebra over an algebraically closed field (Formula Presented) of characteristic p > 2. A module of g is said to be of Kac–Weisfeiler type if its dimension coincides with the dimensional lower bound in the super Kac–Weisfeiler property presented by Wang–Zhao in [9]. In this paper, we verify the existence of the Kac–Weisfeiler modules for gl_m|_n. We also establish the corresponding consequence for the special linear Lie superalgebra sl_m|_n with the restrictions that p > 2 and p ∤ (m - n).

Original language	English
Pages (from-to)	471-490
Number of pages	20
Journal	Israel Journal of Mathematics
Volume	214
Issue number	1
DOIs	https://doi.org/10.1007/s11856-016-1338-1
State	Published - 1 Jul 2016

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abstract = "Let g:= glm|n be a general linear Lie superalgebra over an algebraically closed field (Formula Presented) of characteristic p > 2. A module of g is said to be of Kac–Weisfeiler type if its dimension coincides with the dimensional lower bound in the super Kac–Weisfeiler property presented by Wang–Zhao in [9]. In this paper, we verify the existence of the Kac–Weisfeiler modules for glm|n. We also establish the corresponding consequence for the special linear Lie superalgebra slm|n with the restrictions that p > 2 and p ∤ (m - n).",

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AU - Shu, Bin

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N2 - Let g:= glm|n be a general linear Lie superalgebra over an algebraically closed field (Formula Presented) of characteristic p > 2. A module of g is said to be of Kac–Weisfeiler type if its dimension coincides with the dimensional lower bound in the super Kac–Weisfeiler property presented by Wang–Zhao in [9]. In this paper, we verify the existence of the Kac–Weisfeiler modules for glm|n. We also establish the corresponding consequence for the special linear Lie superalgebra slm|n with the restrictions that p > 2 and p ∤ (m - n).

AB - Let g:= glm|n be a general linear Lie superalgebra over an algebraically closed field (Formula Presented) of characteristic p > 2. A module of g is said to be of Kac–Weisfeiler type if its dimension coincides with the dimensional lower bound in the super Kac–Weisfeiler property presented by Wang–Zhao in [9]. In this paper, we verify the existence of the Kac–Weisfeiler modules for glm|n. We also establish the corresponding consequence for the special linear Lie superalgebra slm|n with the restrictions that p > 2 and p ∤ (m - n).

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On Kac–Weisfeiler modules for general and special linear lie superalgebras

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