Unitary representations of rational Cherednik algebras

Stephen Griffeth (U Edinburgh)

Wednesday 10th February, 2010 16:00-17:00 204


The rational Cherednik algebra attached to a complex reflection group G is in many ways analogous to the enveloping algebra of a semisimple Lie algebra. In particular, there is a well-behaved "category O", whose irreducible objects are indexed by the irreducible complex representations of G, and each such irreducible comes with a non-degenerate contravariant Hermitean form. A natural problem, suggested by Ivan Cherednik, is to classify those irreducibles whose contravariant form is positive definite. I'll discuss the solution to this problem for the symmetric group S_n, and how the approach should generalize to deal with the infinite family G(r,p,n) of complex reflection groups. Time permitting, we'll also discuss applications of the same technique to other representation theoretic questions. (Joint work with Pavel Etingof, Emanuel Stoica, and Charles Dunkl)

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