Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Infinitesimal Cherednik algebras are continuous analogues of rational Cherednik algebras, and in the case of $\mathfrak {gl}_n$, are deformations of universal enveloping algebras of the Lie algebras $\mathfrak {sl}_{n+1}$. 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 $H_\zeta (\mathfrak {gl}_n)$. In the second half, we investigate Poisson-analogues of the infinitesimal Cherednik algebras and generalize various results to $H_\zeta (\mathfrak {sp}_{2n})$, including Kostant’s theorem.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 17B10

Retrieve articles in all journals with MSC (2010): 17B10

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

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

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.