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arXiv · 2211.03139

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

Quan Situ
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Abstract

We establish an algebra isomorphism between the center of the category $\mathcal{O}$ for a hybrid quantum group at a root of unity $ζ$ and the cohomology of $ζ$-fixed locus on affine Grassmannian. A deformed version of this isomorphism was established in the previous paper of the author. For the Steinberg block of $\mathcal{O}$, we construct an abelian equivalence to the category of equivariant sheaves on the Springer resolution.

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Quan Situ. 2026-01-23. Center of the category $\mathcal{O}$ for a hybrid quantum group. https://arxiv.org/abs/2211.03139

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