Classification of simple strong Harish-Chandra $W(m,n)$-modules

Abstract

We classify all simple strong Harish-Chandra modules for the Lie superalgebra $W(m,n)$. We show that every such module is either strongly cuspidal or a module of the highest weight type. We construct tensor modules for $W(m,n)$, which are parametrized by simple finite-dimensional $gl(m,n)$-modules and show that every simple strongly cuspidal $W(m,n)$-module is a quotient of a tensor module. Finally, we realize modules of the highest weight type as simple quotients of the generalized Verma modules induced from tensor modules for $W(m-1,n)$.

After this paper was completed, we learned about a recent preprint by Yaohui Xu and Rencai Lu, arXiv:2001.04089 [math.RT], where the same results were obtained

References in corpus (1)

• Supports of weight modules over Witt algebras

Cited by in corpus (3)

• Classification of simple Harish-Chandra modules over the N=1 Ramond algebra
• bounded weight modules over the Lie superalgebra of Cartan W-type
• Classification of simple strong Harish-Chandra modules over the Lie superalgebra of vector fields on $\C^{m|n}$