论文标题
惠特克类别，正确分层的类别和谎言的Fock空间分类
Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras
论文作者
论文摘要
我们研究了I型I型惠特克模块的各种类别的超级甲壳虫，被认为是适合正确分层类别框架的凝聚力类别。这些类别是Baceelin functor $γ_ζ$的目标。我们表明，可以将这些类别描述为等效性，是BGG类别$ \ MATHCAL O $的Serre serre，以及Harish-Chandra $的某些单数类别（\ Mathfrak G，\ Mathfrak g _ {\ bar 0}）$ - bimodules。我们还表明$γ_ζ$是Serre商函子的实现。我们进一步研究了A型A型组上的$ Q $ -Symetized Fock空间，并证明，对于一般线性而言，我们的whittaker类别，函数$γ_ζ$以及各种serre serre vertients和serre vortient functient functors的实现，分类此$ q $ q $ q $ q $ q $ q-smymetrized $ q $ $ $ $ - $ smmertmmmermemmmmmermemermemmmmermemmmmermemmmmermemermemmermemmermemmermemmmmmermemerize。在这张图片中，在此$ q $ symetrized的fock空间中的规范和双重规范基础分别对应于这些Whittaker类别中的倾斜和简单对象。
We study various categories of Whittaker modules over a type I Lie superalgebra realized as cokernel categories that fit into the framework of properly stratified categories. These categories are the target of the Backelin functor $Γ_ζ$. We show that these categories can be described, up to equivalence, as Serre quotients of the BGG category $\mathcal O$ and of certain singular categories of Harish-Chandra $(\mathfrak g,\mathfrak g_{\bar 0})$-bimodules. We also show that $Γ_ζ$ is a realization of the Serre quotient functor. We further investigate a $q$-symmetrized Fock space over a quantum group of type A and prove that, for general linear Lie superalgebras our Whittaker categories, the functor $Γ_ζ$ and various realizations of Serre quotients and Serre quotient functors categorify this $q$-symmetrized Fock space and its $q$-symmetrizer. In this picture, the canonical and dual canonical bases in this $q$-symmetrized Fock space correspond to tilting and simple objects in these Whittaker categories, respectively.
