Traces and Supertraces on Symplectic Reflection Algebras

Abstract

The symplectic reflection algebra H_1,ν (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 ν. We present values of T(G) and S(G) for the groups generated by the root systems and for the groups G = Γ ≀ S_N, where Γ is a finite subgroup of S_p(2,ℂ).