On Kac-Weisfeiler modules for general and special linear Lie superalgebras

2014/12/21 by Yang Zeng, Zeng, Yang, Bin Shu +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1412.6802

Abstract

Let \ggg:=\gl_m|n be a general linear Lie superalgebra over an algebraically closed field \mathdsk=\mathbbF_p of characteristic p>2. A module of \ggg is said to be of Kac-Weisfeiler if its dimension coincides with the dimensional lower bound in the super Kac-Weisfeiler property presented by Wang-Zhao in \citeWZ. 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 superalgebras \mathfraksl_m|n with restrictions p>2 and p\nmid(m-n).

Related

• A proof of the first Kac-Weisfeiler conjecture in large characteristics
• On simple modules for the restricted Lie superalgebra gl(m|n)
• Representations of Lie superalgebras in prime characteristic III
• Modular representations of strange classical Lie superalgebras and the first super Kac-Weisfeiler conjecture
• Finite W-superalgebras and the dimensional lower bounds for the representations of basic Lie superalgebras