Description
The celebrated work of De Concini–Kac–Procesi established that the representation theory of quantum groups at roots of unity is closely linked to the conjugacy classes of the underlying group. In this talk, we extend this approach to quantum symmetric pairs.
For an i-quantum group $U^\imath$ associated with an involution θ, we consider a De Concini–Kac type integral form and study its specialization $U^\imath_ε$ at an odd root of unity. We show that the simple modules of $U^\imath_ε$ are parametrized by θ-twisted conjugacy classes of the underlying group and provide an explicit upper bound on their dimensions. Moreover, this bound is attained for simple modules corresponding to generic twisted conjugacy classes. Along the way, we construct a finite-dimensional coideal subalgebra of the Lusztig small quantum group.
This is joint work with Weinan Zhang.