Unitary representations of rational Cherednik algebras and Hecke algebras
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2011
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| Online Access: | http://hdl.handle.net/1721.1/64606 |
| _version_ | 1826202444886966272 |
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| author | Stoica, Emanuel (Emanuel I.) |
| author2 | Pavel Etingof. |
| author_facet | Pavel Etingof. Stoica, Emanuel (Emanuel I.) |
| author_sort | Stoica, Emanuel (Emanuel I.) |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. |
| first_indexed | 2024-09-23T12:07:34Z |
| format | Thesis |
| id | mit-1721.1/64606 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T12:07:34Z |
| publishDate | 2011 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/646062019-04-11T10:23:14Z Unitary representations of rational Cherednik algebras and Hecke algebras Stoica, Emanuel (Emanuel I.) Pavel Etingof. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. Cataloged from PDF version of thesis. Includes bibliographical references (p. 49-50). We begin the study of unitary representations in the lowest weight category of rational Cherednik algebras of complex reflection groups. We provide the complete classification of unitary representations for the symmetric group, the dihedral group, as well as some additional partial results. We also study the unitary representations of Hecke algebras of complex reflection groups and provide a complete classification in the case of the symmetric group. We conclude that the KZ functor defined in [16] preserves unitarity in type A. Finally, we formulate a few conjectures concerning the classification of unitary representations for other types and the preservation of unitarity by the KZ functor and the restriction functors defined in [2]. by Emanuel Stoica. Ph.D. 2011-06-20T15:59:16Z 2011-06-20T15:59:16Z 2010 2010 Thesis http://hdl.handle.net/1721.1/64606 727146279 eng 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 50 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Stoica, Emanuel (Emanuel I.) Unitary representations of rational Cherednik algebras and Hecke algebras |
| title | Unitary representations of rational Cherednik algebras and Hecke algebras |
| title_full | Unitary representations of rational Cherednik algebras and Hecke algebras |
| title_fullStr | Unitary representations of rational Cherednik algebras and Hecke algebras |
| title_full_unstemmed | Unitary representations of rational Cherednik algebras and Hecke algebras |
| title_short | Unitary representations of rational Cherednik algebras and Hecke algebras |
| title_sort | unitary representations of rational cherednik algebras and hecke algebras |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/64606 |
| work_keys_str_mv | AT stoicaemanuelemanueli unitaryrepresentationsofrationalcherednikalgebrasandheckealgebras |