Representations of rational Cherednik algebras of rank 1 in positive characteristic

2003/07/31 by Frédéric Latour, Latour, Frédéric · 2 citations
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Polynomial and algebraic computation #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.math/0307390

12 pages

arxiv created 2003/07/31 · openalex publication_date 2003/07/31 · 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 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.

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• Representations of Cherednik Algebras Associated to Symmetric and Dihedral Groups in Positive Characteristic
• Representations of trigonometric Cherednik algebras of rank 1 in positive characteristic

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