Abstract:In this talk, we will introduce a quantum analogue of the BGG category O, which is the category O for the hybrid quantum group introduced by Gaitsgory. We show that the principal block of quantum category O is a version of the affine Hecke category. More precisely, the principal block is abelian equivalent to a category of coherent sheaves involving the Springer resolution and its non-...
Abstract:I will give a brief introduction to quantum groups and their representation theory with the emphasis on applications to integrable systems. If time permits, I will talk about positive representations and their Clebsch-Gordan coefficients and Racah-Wigner coefficients in the case of U_q(sl_2)