论文标题
卡坦W型的谎言超级骨架上的有界重量模块
bounded weight modules over the Lie superalgebra of Cartan W-type
论文作者
论文摘要
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 $A_{m,n}$.在本文中，我们将非平凡的简单有限权重$ w_ {m，n} $模块相对于$ w_ {m，n} $的标准cartan代数。任何此类模块都是张量模块$ f（p，l（v_1 \ otimes v_2））$的简单商，对于简单的重量模块$ p $，weyl superalgebra $ \ mathcal k_ {m，n} $，一个有限量的简单$ \ gl_mm $ -mmodule $ v_1 $ $ v_1 $ v_ $ v_ $ v_- $ v_- $ v_ $ v_-mm
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 $V_2$.
