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arXiv · 2211.03130

On the category $\mathcal{O}$ of a hybrid quantum group

Quan Situ
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Abstract

We study the representation theory of a hybrid quantum group at root of unity $\zeta$ 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 $\zeta$-fixed locus on the affine Grassmannian attached to the Langlands dual group.

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Quan Situ. 2022-11-06. On the category $\mathcal{O}$ of a hybrid quantum group. https://arxiv.org/abs/2211.03130

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