On the category \(\mathcal{O}\) of a hybrid quantum group (Q6639758)

This paper concerns about the representation theory of a hybrid quantum group at root of unity \(\zeta\) introduced by Gaitsgory. The author studies deformations of the category \(\mathcal{O}\). For subgeneric deformations, he constructs the endomorphism algebra of big projective object and compute it explicitly. The 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.