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.
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