DMCA
Cherednik algebras and differential operators on quasi-invariants
Cached
Download Links
| Venue: | Duke Math. J |
| Citations: | 67 - 12 self |
BibTeX
@ARTICLE{Berest_cherednikalgebras,
author = {Yuri Berest and Pavel Etingof and Victor Ginzburg},
title = {Cherednik algebras and differential operators on quasi-invariants},
journal = {Duke Math. J},
year = {},
pages = {2004--16039}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
We develop representation theory of the rational Cherednik algebra Hc associated to a finite Coxeter group W in a vector space h, and a parameter “c. ” We use it to show that, for integral values of “c, ” the algebra Hc is simple and Morita equivalent to D(h)#W, the cross product of W with the algebra of polynomial differential operators on h. O. Chalykh, M. Feigin, and A. Veselov [CV1], [FV] introduced an algebra, Qc, of quasi-invariant polynomials on h, such that C[h] W ⊂ Qc ⊂ C[h]. We prove that the algebra D(Qc) of differential operators on quasi-invariants is a simple algebra, Morita equivalent to D(h). The subalgebra D(Qc) W ⊂ D(Qc) of W-invariant operators turns out to be isomorphic to the spherical subalgebra eHce ⊂ Hc. We show that D(Qc) is generated, as an algebra, by Qc and its “Fourier dual ” Q ♭ c, and that D(Qc) is a rank-one projective (Qc ⊗ Q ♭ c)-module (via multiplication-action on D(Qc) on opposite sides).
Keyphrases
differential operator cherednik algebra morita equivalent integral value rank-one projective polynomial differential operator opposite side spherical subalgebra ehce hc veselov cv1 simple algebra cross product rational cherednik algebra hc representation theory fourier dual finite coxeter group vector space algebra hc w-invariant operator quasi-invariant polynomial
