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SUMMARY:Chevalley restriction theorem for vector-valued functions on quant
 um groups - Martina Balagovic (York)
DTSTART:20130220T163000Z
DTEND:20130220T173000Z
UID:TALK43168@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:For a simple finite dimensional Lie algebra g\, its Cartan sub
 algebra h and\nits Weyl group W\, the classical Chevalley theorem states t
 hat\, by\nrestricting ad-invariant polynomials on g to its Cartan subalgeb
 ra\, one\nobtains all W-invariant polynomials on h\, and the resulting res
 triction map\nis an isomorphism. I will explain how to generalize this sta
 tement to the\ncase when a Lie algebra is replaced by a quantum group\, an
 d the target\nspace of the polynomial maps is replaced by a finite dimensi
 onal\nrepresentation of this quantum group. I will describe all prerequisi
 tes for\nstating the theorem and sketch the idea of the proof\, most notab
 ly the\nnotion of dynamical Weyl group introduced by Etingof and Varchenko
 .\n
LOCATION:MR12
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