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

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. [ABSTRACT FROM AUTHOR]