Representations of the rational Cherednik algebra $H_{t,c}(S_3,\text{h})$ in positive characteristic

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