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We study the rational Cherednik algebra $H_{t,c}(S_3,\h)$ of type $A_2$ inpositive 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 gradedsubmodule of the Verma module.

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