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

Abstract

In this paper, we classify simple strong Harish-Chandra modules over the Lie superalgebra $W_{m,n}$ of vector fields on $\C^{m|n}$. Any such module is the unique simple submodule of some tensor module $F(P,V)$ for a simple weight module $P$ over the Weyl superalgebra ${\mathcal{K}}_{m,n}$ and a simple weight module $V$ over the general linear superalgebra $\gl_{m,n}$.

A typo in abstract is corrected

References in corpus (5)

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