论文标题
简单强的Harish-Chandra $ W（m，n）$的分类 - 模块
Classification of simple strong Harish-Chandra $W(m,n)$-modules
论文作者
论文摘要
我们将所有简单的Harish-Chandra模块分类为Lie Superalgebra $ W（m，n）$。我们表明，每个这样的模块都是强烈的尖端或最高权重类型的模块。我们为$ w（m，n）$构造张量模块，该模块由简单的有限尺寸$ gl（m，n）$ - 模块进行参数化，并表明每个简单的cuspidal $ w（m，n）$ - 模块都是张量模块的商。最后，我们将重量类型的最高权重模块视为从张量模块（M-W（M-1，N）$的张量模块引起的广义VERMA模块的简单商。
We classify all simple strong Harish-Chandra modules for the Lie superalgebra $W(m,n)$. We show that every such module is either strongly cuspidal or a module of the highest weight type. We construct tensor modules for $W(m,n)$, which are parametrized by simple finite-dimensional $gl(m,n)$-modules and show that every simple strongly cuspidal $W(m,n)$-module is a quotient of a tensor module. Finally, we realize modules of the highest weight type as simple quotients of the generalized Verma modules induced from tensor modules for $W(m-1,n)$.
