Work

On the category 𝒪 of a hybrid quantum group

Year: 2024

Type: article

Abstract: We study the representation theory of a hybrid quantum group at root of unity ζ \zeta introduced by Gaitsgory. After discussing some basic properties of its category O \mathcal {O} , we study deformations of the category O \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 O \mathcal {O} and the equivariant cohomology of ζ \zeta -fixed locus on the affine Grassmannian attached to the Langlands dual group.

Source: Representation Theory of the American Mathematical Society

DOI: 10.1090/ert/676

Author: Quan Situ

Institution: Tsinghua University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4403486426

FWCI: 0.673

Cites: 14

Cited by: 1

Related to: 10