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A Lie-theoretic construction of some representations of the degenerate affine and double affine Hecke algebras of type $ BC_n$


Authors: Pavel Etingof, Rebecca Freund and Xiaoguang Ma
Journal: Represent. Theory 13 (2009), 33-49
MSC (2000): Primary 16G99
DOI: https://doi.org/10.1090/S1088-4165-09-00345-8
Published electronically: February 23, 2009
MathSciNet review: 2480387
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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 [Enhancements On Off] (What's this?)

  • [AS] T. Arakawa, T. Suzuki, Duality between $ \mathfrak{sl}_n(\mathbb{C})$ and the degenerate affine Hecke algebra, J. Algebra 209 (1998), no. 1, 288-304. MR 1652134 (99h:17005)
  • [CEE] D. Calaque, B. Enriquez, P. Etingof, Universal KZB equations I: the elliptic case, arXiv:math/0702670.
  • [Ch] I. Cherednik, Double Affine Hecke Algebras, London Math. Soc. Lect. Note Ser. 319, Cambridge University, 2005. MR 2133033 (2007e:32012)
  • [Dri] V. Drinfeld, Degenerate affine Hecke algebras and Yangians (Russian), Funktsional. Anal. i Prilozhen. 20 (1986), no. 1, 69-70. MR 831053 (87m:22044)
  • [Lus] G. Lusztig, Affine Hecke algebra and their graded version, J. Amer. Math. Soc. 2 (1989), no. 3, 599-635. MR 991016 (90e:16049)
  • [M] X. Ma, On some representations of degenerate affine Hecke algebras of type $ BC_{n}$, arXiv:0810.0791.
  • [RS] A. Ram, A.V. Shepler, Classification of graded Hecke algebras for complex reflection groups, Comment. Math. Helv. 78 (2003), no. 2, 308-334. MR 1988199 (2004d:20007)

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Additional Information

Pavel Etingof
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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

DOI: https://doi.org/10.1090/S1088-4165-09-00345-8
Received by editor(s): January 10, 2008
Received by editor(s) in revised form: October 14, 2008
Published electronically: February 23, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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