## 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
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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

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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