Irreducible representations and decomposition matrices for rational Cherednik algebras

Expositor: Emily Norton. Kansas State University

Jueves 12 de marzo a las 16:00 hrs.
Sala de magíster.

Resumen: Rational Cherednik algebras H_c(W) have a representation theory that echoes that of semisimple complex Lie algebras, in that there is a highest weight category of «nice» representations, Category O, containing Verma modules which have unique simple quotients. In particular, all the simple representations belong to this category and they are indexed by the simple representations of the underlying complex reflection group W. The characters of simple representations can be found from the decomposition matrix, which encodes the multiplicities of simples in the composition series of Vermas. I will survey what is known for W a real reflection group, and how to explicitly find these decomposition matrices when W is one of the exceptional real reflection groups (type E, F, and H).