Representations of rational Cherednik algebras and quantum integrable systems

Misha Feigin (Glasgow University)

Wednesday 26th November, 2008 16:00-17:00 Mathematics Building, room 214


The rational Cherednik algebra is determined by a finite Coxeter group and an invariant multiplicity function on the roots. A natural category of the representations is semisimple for generic multiplicities, and the simple modules are parametrized by the irreducible representations of the Coxeter group. When multiplicity is special already the representation on the polynomials (the one corresponding to the trivial representation of the Coxeter group) may become reducible. I'll discuss special submodules in the polynomial representation. These submodules form radical ideals in the ring of polynomials and they are determined by parabolic subgroups in the original Coxeter group. These parabolic subgroups can be explicitely specified. I'll also discuss quantum integrable systems of Calogero-Moser type which can be associated to such submodules in the polynomial representation.

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