The number of independent Traces and Supertraces on the Symplectic Reflection Algebra $H_{1, u}(Gamma wr S_N)$

Symplectic reflection algebra $ H_{1, , u}(G)$ has a $T(G)$-dimensional space of traces whereas, when considered as a superalgebra with a natural parity, 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 do not depend on the parameter $ u$. In this paper, the values $T(G)$ and $S(G)$ are explicitly calculated for the groups $G= Gamma wr S_N$, where $Gamma$ is a finite subgroup of $Sp(2,mathbb C)$.