Representations of infinitesimal Cherednik algebras

Authors:
Fengning Ding and Alexander Tsymbaliuk

Journal:
Represent. Theory **17** (2013), 557-583

MSC (2010):
Primary 17B10

Published electronically:
November 5, 2013

MathSciNet review:
3123740

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Abstract | References | Similar Articles | Additional Information

Abstract: Infinitesimal Cherednik algebras are continuous analogues of rational Cherednik algebras, and in the case of , are deformations of universal enveloping algebras of the Lie algebras . In the first half of this paper, we compute the determinant of the Shapovalov form, enabling us to classify all irreducible finite dimensional representations of . In the second half, we investigate Poisson-analogues of the infinitesimal Cherednik algebras and generalize various results to , including Kostant's theorem.

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Additional Information

**Fengning Ding**

Affiliation:
Phillips Academy, 180 Main St., Andover, Massachusetts 01810

Address at time of publication:
Department of Mathematics, Harvard College, Cambridge, Massachusetts 02138

Email:
fding@college.harvard.edu

**Alexander Tsymbaliuk**

Affiliation:
Independent University of Moscow, 11 Bol’shoy Vlas’evskiy per., Moscow 119002, Russia

Address at time of publication:
Department of Mathematics, MIT, 77 Massachusetts Ave., Cambridge, Massachusetts 02139

Email:
sasha{\textunderscore}ts@mit.edu

DOI:
http://dx.doi.org/10.1090/S1088-4165-2013-00443-0

Received by editor(s):
October 21, 2012

Received by editor(s) in revised form:
February 26, 2013, March 30, 2013, and July 31, 2013

Published electronically:
November 5, 2013

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.