Representations of trigonometric Cherednik algebras of rank 1 in positive characteristic

Details Representations of trigonometric Cherednik algebras of rank 1 in positive characteristic Representations of trigonometric Cherednik algebras of rank 1 in positive characteristic

2004-01-27

arxiv.org/abs/math/0401387v1

Mathematics

Representation Theory

19 pages

Scientific paper

In this paper, we classify the irreducible representations of the trigonometric 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 2p. In this case, smaller representations exist if and only if the "coupling constant" k is in F_p; namely, if 0 <= k <= p-1, then there exist irreducible representations of dimensions p-k and p+k. The other case is the "classical" case, where "Planck's constant" is zero and generic irreducible representations have dimension 2p. In that case, one-dimensional representations exist if and only if the "coupling constant" k is zero.

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