Chevalley restriction theorem for vector-valued functions on quantum groups

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• Martina Balagovic (York)
• Wednesday 20 February 2013, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Christopher Brookes.

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 statement 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 notion of dynamical Weyl group introduced by Etingof and Varchenko.

This talk is part of the Algebra and Representation Theory Seminar series.

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