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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.

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A Lie-theoretic construction of some representations of the degenerate affine and double affine Hecke algebras of type $BC_n$
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by Pavel Etingof, Rebecca Freund and Xiaoguang Ma
Represent. Theory 13 (2009), 33-49
DOI: https://doi.org/10.1090/S1088-4165-09-00345-8
Published electronically: February 23, 2009

Abstract:

Let $G=GL(N)$, $K=GL(p)\times GL(q)$, where $p+q=N$, and let $n$ be a positive integer. We construct a functor from the category of Harish-Chandra modules for the pair $(G,K)$ to the category of representations of the degenerate affine Hecke algebra of type $B_n$, and a functor from the category of $K$-monodromic twisted $D$-modules on $G/K$ to the category of representations of the degenerate double affine Hecke algebra of type $BC_n$; the second functor is an extension of the first one.
References
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Bibliographic Information
  • Pavel Etingof
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 289118
  • Email: etingof@math.mit.edu
  • Rebecca Freund
  • Affiliation: Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • Email: rlfreund@mit.edu
  • Xiaoguang Ma
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • Email: xma@math.mit.edu
  • Received by editor(s): January 10, 2008
  • Received by editor(s) in revised form: October 14, 2008
  • Published electronically: February 23, 2009
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 13 (2009), 33-49
  • MSC (2000): Primary 16G99
  • DOI: https://doi.org/10.1090/S1088-4165-09-00345-8
  • MathSciNet review: 2480387