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