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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Representations of infinitesimal Cherednik algebras
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by Fengning Ding and Alexander Tsymbaliuk
Represent. Theory 17 (2013), 557-583
Published electronically: November 5, 2013


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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Bibliographic 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