2026-09-20T01:31:37Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/301462022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Pavel Etingof.
Latour, Frédéric
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2006-03-24T18:23:50Z
2006-03-24T18:23:50Z
2004
2004
http://hdl.handle.net/1721.1/30146
56018269
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.
68 p.
1613763 bytes
1613568 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Representations of Cherednik algebras in positive characteristic
Thesis
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<Abstract>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.</Abstract>
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