University of Sydney Algebra Seminar
Michael Ehrig
Friday 21 October, 12-1pm, Place: Carslaw 173
Quantum symmetric pairs and representations of quantum groups at a root of unity
It is well known that one can define a simple action of the quantized universal enveloping algebra of infinite matrices on the Fock space. Via highest weight theory one can embed the Grothendieck group of finite dimensional representations of the quantum group of type A at a root of unity into this space and compare the action on the Fock space with the action of certain functors on the Grothendieck group. In type A, this gives a relationship between the action of these functors and an action of a quantized Kac-Moody algebra that can be obtained from the simple action on the Fock space. In this talk, I will discuss what the situation is if one replaces the quantum group of type A with of a quantum group of classical type B/C/D. This is joint work with Kaixuan Gan.