Quasi-Invariants of Complex Reflection Groups

Details Quasi-Invariants of Complex Reflection Groups Quasi-Invariants of Complex Reflection Groups

2009-12-23

arxiv.org/abs/0912.4518v2

Mathematics

Representation Theory

38 pages, final version, to appear in Compositio Math

Scientific paper

We introduce quasi-invariant polynomials for an arbitrary finite complex reflection group W. Unlike in the Coxeter case, the space Q_k of quasi-invariants of a given multiplicity is not, in general, an algebra but a module over the coordinate ring of some (singular) affine variety X_k. We extend the main results of Etingof, Ginzburg and the first author (see [BEG]) to this setting: in particular, we show that the variety X_k and the module Q_k are Cohen-Macaulay, and the rings of differential operators on X_k and Q_k are simple rings, Morita equivalent to the Weyl algebra A_n(C), where n = dim X_k . Our approach relies on representation theory of complex Cherednik algebras and is parallel to that of [BEG]. As a by-product, we prove the existence of shift operators for an arbitrary complex reflection group, confirming a conjecture of Dunkl and Opdam. Another result is a proof of a conjecture of Opdam, concerning certain operations (KZ twists) on the set of irreducible representations of W.

Affiliated with

Also associated with

No associations

Rating

Quasi-Invariants of Complex Reflection Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quasi-Invariants of Complex Reflection Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quasi-Invariants of Complex Reflection Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-362500