## What is a q-reflection group?Add to your list(s) Download to your calendar using vCal - Yuri Bazlov, University of Bath
- Thursday 21 January 2010, 16:00-17:00
- Watson Building, Lecture Room A.
If you have a question about this talk, please contact Simon Goodwin. If or R, reflection groups are the same as Weyl groups, Coxeter groups or complex reflection groups, respectively, and are very important in Lie theory.
We will look at two key properties of a reflection group CG over a field of characteristic 0:*G*-invariants in the polynomial ring*k*[*V*] are themselves a polynomial ring (the Chevalley-Shephard-Todd theorem);- there is a special family of commuting differential-difference operators on
*k*[*V*], called Dunkl operators (they give rise to a rational Cherednik algebra of*G*).
It is interesting to note that the Chevalley-Shephard-Todd theorem (1), which dates back to 1950s, was nontrivially extended to fields of positive characteristic in a more recent work of Serre and Kemper-Malle. In my talk, however, I will remain in characteristic 0 but will be interested in a generalisation of the C-S-T theorem where the polynomial ring is replaced with a noncommutative algebra. I will aim to describe results of myself and Berenstein (inspired by the theory of integrable systems) which lead to a This talk is part of the Algebra seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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