Duality between GL(n,R) and the degenerate affine Hecke algebra for gl(n)

Details Duality between GL(n,R) and the degenerate affine Hecke algebra for gl(n) Duality between GL(n,R) and the degenerate affine Hecke algebra for gl(n)

2009-03-05

arxiv.org/abs/0903.1043v2

Mathematics

Representation Theory

22 pages

Scientific paper

We define an exact functor $F_{n,k}$ from the category of Harish-Chandra
modules for $GL(n,R)$ to the category of finite-dimensional representations for
the degenerate affine Hecke algebra for $gl(k)$. Under certain natural
hypotheses, we prove that the functor maps standard modules to standard modules
(or zero) and irreducibles to irreducibles (or zero).

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