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

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 $F(P,L(V_1\otimes V_2))$ for a simple weight module $P$ over the Weyl superalgebra ${\mathcal{K}}_{m,n}$, a finite-dimensional simple $\gl_m$-module $V_1$ and a simple bounded $\gl_n$-module $V_2$.

References in corpus (4)

• Classification of simple bounded weight modules of the Lie algebra of vector fields on $\C^n$
• Simple weight modules with finite-dimensional weight spaces over Witt superalgebras
• Classification of simple Harish-Chandra modules over the N=1 Ramond algebra
• Classification of simple strong Harish-Chandra $W(m,n)$-modules

Cited by in corpus (1)

• Classification of simple strong Harish-Chandra modules over the Lie superalgebra of vector fields on $\C^{m|n}$