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Representation Theory
Representation Theory
ISSN 1088-4165

 

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
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.


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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: http://dx.doi.org/10.1090/S1088-4165-09-00345-8
PII: S 1088-4165(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.