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

Abstract

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