论文标题
E（5,10）的退化Verma模块的分类
Classification of degenerate Verma modules for E(5,10)
论文作者
论文摘要
给定一个带有subalgebra $ \ frak g _ {\ geq 0} $的谎言superalgebra $ \ frak g $，以及一个有限的二维不可减少的$ \ frak g _ {\ geq 0} $ - 模块 - 模块$ f $ \ otimes_ {u（\ frak g _ {\ geq 0}）} f $称为有限的Verma模块。在本文中，我们将不可误导的有限Verma模块分类为最大的异常线性紧凑型谎言superalgebra $ {\ frak g} = e（5,10）$与subalgebra $ \ frak g _ {\ frak g _ {\ geq 0}的最小密码降低。这是通过对模块$ m（f）$中所有单数矢量的分类来完成的。除了获得1,2,3,4和5度的已知单数矢量外，我们还发现了两个新的单数矢量，分别为7和11。我们表明，有限的1,4,7度的有限的Verma模块的相应形态可以在无限数量的双边Infinite Complexs中排列，其中可能会被视为$ expoffers $ e（5）。
Given a Lie superalgebra $\frak g$ with a subalgebra $\frak g_{\geq 0}$, and a finite-dimensional irreducible $\frak g_{\geq 0}$-module $F$, the induced $\frak g$-module $M(F)=U({\frak g}) \otimes_{U(\frak g_{\geq 0})} F $ is called a finite Verma module. In the present paper we classify the non-irreducible finite Verma modules over the largest exceptional linearly compact Lie superalgebra ${\frak g}=E(5,10)$ with the subalgebra $\frak g_{\geq 0}$ of minimal codimension. This is done via classification of all singular vectors in the modules $M(F)$. Besides known singular vectors of degree 1,2,3,4 and 5, we discover two new singular vectors, of degrees 7 and 11. We show that the corresponding morphisms of finite Verma modules of degree 1,4,7, and 11 can be arranged in an infinite number of bilateral infinite complexes, which may be viewed as 'exceptional' de Rham complexes for $E(5,10)$.
