REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: For a simple finite dimensional Lie algebra g, its Cartan subalgebra h and its Weyl group W, the classical Chevalley theorem
states that by restricting ad-invariant polynomials on g to its Cartan subalgebra, one obtains all W-invariant polynomials on h, and the
resulting restriction map is an isomorphism. I will explain how to generalize this theorem to the case when a Lie algebra is replaced by
a quantum group, and the target space of the polynomial maps is replaced by a finite dimensional representation of this quantum group.
I will describe all prerequisites for stating the theorem and sketch the idea of the proof, most notably the work of Khoroshkin, Nazarov
and Vinberg which this generalizes, and the notion of dynamical Weyl group by Etingof and Varchenko.