Representations of trigonometric Cherednik algebras of rank 1 in positive characteristic

2004/01/27 by Frédéric Latour, Latour, Frédéric
Mathematics · #16G30 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16G30

paper · pdf · doi:10.48550/arxiv.math/0401387

19 pages

arxiv created 2004/01/27 · openalex publication_date 2004/01/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Representations of rational Cherednik algebras of rank 1 in positive characteristic

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