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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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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 PDF
Represent. Theory 13 (2009), 33-49 Request permission

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.
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Additional 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