bounded weight modules over the Lie superalgebra of Cartan W-type

2020/09/27 by Rencai Lü, Lü, Rencai, Yaohui Xue +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2009.12776

Abstract

Let A_m,n be the tensor product of the polynomial algebra in m even variables and the exterior algebra in n odd variables over the complex field \C, and the Witt superalgebra W_m,n be the Lie superalgebra of superderivations of A_m,n. In this paper, we classify the non-trivial simple bounded weight W_m,n modules with respect to the standard Cartan algebra of W_m,n. Any such module is a simple quotient of a tensor module F(P,L(V₁⊗ V₂)) for a simple weight module P over the Weyl superalgebra \mathcal K_m,n, a finite-dimensional simple \gl_m-module V₁ and a simple bounded \gl_n-module V₂.

Citations

• Classification of simple Harish-Chandra modules over the N=1 Ramond algebra

Cited by

• Whittaker Modules for W type Cartan Lie superalgebras

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