A Lie-theoretic construction of some representations of the degenerate affine and double affine Hecke algebras of type 𝐵𝐶_{𝑛}

Etingof, Pavel; Freund, Rebecca; Ma, Xiaoguang

doi:10.1090/S1088-4165-09-00345-8

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.

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