Representations of rational Cherednik algebras of rank one in positive characteristic

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 “Planckʹs 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 “Planckʹs constant” is zero and generic irreducible representations have dimension r.