The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
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| Format: | Thesis |
| Language: | en_US |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/28922 |
| _version_ | 1826215286084206592 |
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| author | Bernhardt, Karen, 1977- |
| author2 | David Vogan. |
| author_facet | David Vogan. Bernhardt, Karen, 1977- |
| author_sort | Bernhardt, Karen, 1977- |
| collection | MIT |
| description | Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005. |
| first_indexed | 2024-09-23T16:21:52Z |
| format | Thesis |
| id | mit-1721.1/28922 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:21:52Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/289222019-04-11T07:14:01Z The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups Bernhardt, Karen, 1977- David Vogan. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. 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. 2005-09-27T19:04:52Z 2005-09-27T19:04:52Z 2005 2005 Thesis http://hdl.handle.net/1721.1/28922 60503798 en_US M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 74 p. 4625319 bytes 4632841 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Bernhardt, Karen, 1977- The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups |
| title | The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups |
| title_full | The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups |
| title_fullStr | The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups |
| title_full_unstemmed | The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups |
| title_short | The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups |
| title_sort | generalized harish chandra homomorphism for hecke algebras of real reductive lie groups |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/28922 |
| work_keys_str_mv | AT bernhardtkaren1977 thegeneralizedharishchandrahomomorphismforheckealgebrasofrealreductiveliegroups AT bernhardtkaren1977 generalizedharishchandrahomomorphismforheckealgebrasofrealreductiveliegroups |