The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups

• Main Author: Bernhardt, Karen, 1977-
• Other Authors: David Vogan.
• Format: Others
• Language: en_US
• Published: Massachusetts Institute of Technology 2005
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/1721.1/28922

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005. === Includes bibliographical references (p. 73-74). === For complex reductive Lie algebras g, the classical Harish-Chandra homomorphism allows to link irreducible finite dimensional representations of g to those of certain subalgebras l. The Casselman-Osborne theorem establishes an extension of this link to infinite dimensional irreducible representations. In this paper we present a generalized Harish-Chandra homomorphism construction for Hecke algebras, and establish the corresponding generalized Casselman-Osborne theorem. This homomorphism can be used to link representations of (g, L n K)-pairs to those of (g, L n K)-pairs, where is a certain subalgebra of g as in the classical case. Since representations of such pairs are closely related to those of the underlying Lie group G, this construction is a good first approximation to lifting the Harish-Chandra homomorphism from the Lie algebra to the Lie group level. === by Karen Bernhardt. === S.M.