The number of independent Traces and Supertraces on the Symplectic Reflection Algebra H1,η(Γ≀SN)

Abstract

Symplectic reflection algebra H1η(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 η.In this paper, the values T(G) and S(G) are explicitly calculated for the groups G = Γ≀SN, where Γ is a finite subgroup of Sp(2,ℂ).