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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Representations of infinitesimal Cherednik algebras
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by Fengning Ding and Alexander Tsymbaliuk PDF
Represent. Theory 17 (2013), 557-583 Request permission


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.
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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:
  • 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:
  • 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
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 17 (2013), 557-583
  • MSC (2010): Primary 17B10
  • DOI:
  • MathSciNet review: 3123740