Representations of the rational Cherednik algebra Ht,c(S3,h) in positive characteristic

Abstract

We study the rational Cherednik algebra $H_{t,c}(S_3,h)$ of type $A_2$ in positive characteristic p, and its irreducible category $O$ representations $L_{t,c}\left(\tau \right)$. For every possible value of $p,t,c$, and τ we calculate the Hilbert polynomial and the character of $L_{t,c}\left(\tau \right)$, and give explicit generators of the maximal proper graded submodule of the Verma module.