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

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

2008-01-09

arxiv.org/abs/0801.1530v4

Represent. Theory 13 (2009), 33--49.

Mathematics

Representation Theory

17 pages, final version. to appear in Representation Theory; mistake about the exactness of the functors are corrected.

Scientific paper

Let G=GL(N), K=GL(p)xGL(q), where p+q=N, and 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. These functors are generalizations of the type A functors from q-alg/9710037 and math/0702670, respectively.

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