2026-09-19T16:02:52Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/289222022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
David Vogan.
Bernhardt, Karen, 1977-
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2005-09-27T19:04:52Z
2005-09-27T19:04:52Z
2005
2005
http://hdl.handle.net/1721.1/28922
60503798
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.
74 p.
4625319 bytes
4632841 bytes
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Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups
Thesis
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