Representations of Cherednik algebras in positive characteristic
Name
56018269-MIT.pdf
Description
Full printable version
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1.54 MB
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ceddac783f8355dd1fbb83ff7eafe7f9
Author(s)
Latour, Frédéric
Advisor(s)
Pavel Etingof.
Date Issued
2004
Publisher
Massachusetts Institute of Technology
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes bibliographical references (p. 67-68).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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