Simple weight modules with finite-dimensional weight spaces over Witt superalgebras

2020/01/13 by Xu, Yaohui, Lü, Rencai · 1 citation
#17B10 #17B20 #17B65 #17B66 #17B68 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2001.04089

Abstract

Let A_m,n be the tensor product of the Laurient polynomial algebra in m even variables and the exterior algebra in n odd variables over the complex field \bC, and the Witt superalgebra W_m,n be the Lie superalgebra of superderivations of A_m,n. In this paper, we classify the simple weight W_m,n modules with finite-dimensional weight spaces with respect to the standard Cartan algebra of W_m,0. Every such module is either a simple quotient of a tensor module or a module of highest weight type.

Cited by

• Whittaker Modules for W type Cartan Lie superalgebras

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