论文标题
在类别上$ \ Mathcal {O} $的混合量子组
On the category $\mathcal{O}$ of a hybrid quantum group
论文作者
论文摘要
我们研究了GaitSgory引入的Unity $ζ$的杂种量子组的表示理论。在讨论其类别$ \ Mathcal {O} $的一些基本属性之后，我们研究了类别$ \ Mathcal {O} $的变形。对于亚类变形，我们构建了大型投影对象的内态代数，并明确计算它。我们的主要结果是在变形类别$ \ Mathcal {O} $的中心与$ζ$固定的基因座的同构中心之间的代数同构。
We study the representation theory of a hybrid quantum group at root of unity $ζ$ introduced by Gaitsgory. After discussing some basic properties of its category $\mathcal{O}$, we study deformations of the category $\mathcal{O}$. For subgeneric deformations, we construct the endomorphism algebra of big projective object and compute it explicitly. Our main result is an algebra isomorphism between the center of deformed category $\mathcal{O}$ and the equivariant cohomology of $ζ$-fixed locus on the affine Grassmannian attached to the Langlands dual group.
