Representations of Cherednik algebras in positive characteristic
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2006
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| Online Access: | http://hdl.handle.net/1721.1/30146 |
| _version_ | 1826217646244233216 |
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| author | Latour, Frédéric |
| author2 | Pavel Etingof. |
| author_facet | Pavel Etingof. Latour, Frédéric |
| author_sort | Latour, Frédéric |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004. |
| first_indexed | 2024-09-23T17:06:59Z |
| format | Thesis |
| id | mit-1721.1/30146 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T17:06:59Z |
| publishDate | 2006 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/301462019-04-11T06:10:53Z Representations of Cherednik algebras in positive characteristic Latour, Frédéric 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, 2004. Includes bibliographical references (p. 67-68). In this thesis, we first classify the irreducible representations of the rational Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. One is the "quantum" case, where "Planck's constant" is nonzero and generic irreducible representations have dimension pr, where r is the order of the cyclic group contained in the algebra. The other is the "classical" case, where "Planck's constant" is zero and generic irreducible representations have dimension r. Secondly, we classify the irreducible representations of the trigonometric Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. In one case, the "Planck's constant" is zero, and generic irreducible representations have dimension 2; one-dimensional irreducible representations exist when the "coupling constant" is also zero. In the other case, the "Planck's constant" is nonzero, and generic irreducible representations have dimension 2p; if the "coupling constant" is an even integer 0 =/< k =/< p - 1, then there exist smaller irreducible representations of dimensions p + k and p - k. by Frédéric Latour. Ph.D. 2006-03-24T18:23:50Z 2006-03-24T18:23:50Z 2004 2004 Thesis http://hdl.handle.net/1721.1/30146 56018269 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 68 p. 1613763 bytes 1613568 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Latour, Frédéric Representations of Cherednik algebras in positive characteristic |
| title | Representations of Cherednik algebras in positive characteristic |
| title_full | Representations of Cherednik algebras in positive characteristic |
| title_fullStr | Representations of Cherednik algebras in positive characteristic |
| title_full_unstemmed | Representations of Cherednik algebras in positive characteristic |
| title_short | Representations of Cherednik algebras in positive characteristic |
| title_sort | representations of cherednik algebras in positive characteristic |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/30146 |
| work_keys_str_mv | AT latourfrederic representationsofcherednikalgebrasinpositivecharacteristic |