Description
Using Tannaka-Krein methods, a duality can be constructed between actions of a compact quantum group on the one hand, and module C*-categories over its representation category on the other. In this talk, we will construct three module C*-categories for the q-deformed representation category of a compact semisimple Lie group G, starting from a compact symmetric space G/K for G. The first construction is based on the theory of cyclotomic KZ-equations developed by B. Enriquez. The second construction uses the notion of quantumsymmetric pair as developed by G. Letzter. The third construction uses the notion of twisted Heisenberg algebra. In all cases, we show that the module C*-category is twist-braided - this is due to B. Enriquez in the first case, S.
Kolb in the second case, and closely related to work of J. Donin, P.Kulish and A. Mudrov in the third case. We formulate a conjecture concerning equivalence of these twist-braided module C*-categories, and prove the equivalence in the simplest case of quantum SU(2). This is joint work with S.Neshveyev, L. Tuset and M. Yamashita.
| Period | 25 Jan 2018 |
|---|---|
| Event title | Workshop Tensor categories, Hopf algebras and quantum groups |
| Event type | Workshop |
| Location | Marburg, Germany |
| Degree of Recognition | International |