Representations of rational Cherednik algebras of rank one in positive characteristic
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 .