Traces and supertraces on the symplectic reflection algebras

The symplectic reflection algebra $H_{1,\nu}(G)$ has a $T(G)$-dimensional space of traces, and if it is regarded as a superalgebra with a natural parity, then it has an $S(G)$-dimensional space of supertraces. The values of $T(G)$ and $S(G)$ depend on the symplectic reflection group $G$ and are independent of the parameter $\nu$. We present values of $T(G)$ and $S(G)$ for the groups generated by the root systems and for the groups $G=\Gamma\wr S_N$, where $\Gamma$ is a finite subgroup of $Sp(2,\mathbb C)$.