Bounded Weight Modules Over the Lie Superalgebra of Cartan W-type

Let Am,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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {C}$\end{document}, and the Witt superalgebra Wm,n be the Lie superalgebra of superderivations of Am,n. In this paper, we classify the non-trivial simple bounded weight Wm,n modules with respect to the standard Cartan subalgebra of Wm,n. Any such module is a simple quotient of a tensor module F(P,L(V1 ⊗ V2)) for a simple weight module P over the Weyl superalgebra Km,n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {K}_{m,n}$\end{document}, a finite-dimensional simple glm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak {gl}_{m}$\end{document}-module V1 and a simple bounded gln\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak {gl}_{n}$\end{document}-module V2.