论文标题
惠特克（Whittaker
Whittaker categories of quasi-reductive Lie superalgebras and quantum symmetric pairs
论文作者
论文摘要
我们表明，对于具有三角形分解和nilpotent自由基的字符$ζ$的任意准重新级别的超级超级甲壳虫，只要存在后者，相关的backelin functor $γ_ζ$将Verma模块发送到标准惠特克模块。结果，这为确定标准Whittaker模块的组成因子的问题提供了一个完整的解决方案，从类别中的Verma模块的组成因子$ \ MATHCAL O $中。在Ortho-Splectic Lie SuperAlgebras的情况下，我们表明Baceelin functor $γ_ζ$及其目标类别分别对$ q $ -Symmetrizing Map和相应的$ Q $ q $ symemetized fock空间进行分类，并与Quasi-Split量子量子符合量子$ Aiii $ Aiii $。
We show that, for an arbitrary quasi-reductive Lie superalgebra with a triangular decomposition and a character $ζ$ of the nilpotent radical, the associated Backelin functor $Γ_ζ$ sends Verma modules to standard Whittaker modules provided the latter exist. As a consequence, this gives a complete solution to the problem of determining the composition factors of the standard Whittaker modules in terms of composition factors of Verma modules in the category $\mathcal O$. In the case of the ortho-symplectic Lie superalgebras, we show that the Backelin functor $Γ_ζ$ and its target category, respectively, categorify a $q$-symmetrizing map and the corresponding $q$-symmetrized Fock space associated with a quasi-split quantum symmetric pair of type $AIII$.
