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 | References | Similar Articles | Additional Information

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

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.