Ideals Generated by Traces or by Supertraces in the Symplectic Reflection Algebra H1,V(I2(2m + 1)) II

Abstract

The algebra ℋ:=H1,v(I2(2m + 1)) of observables of the Calogero model based on the root system I2(2m + 1) has an m-dimensional space of traces and an (m + 1)-dimensional space of supertraces. In the preceding paper we found all values of the parameter ν for which either the space of traces contains a degenerate nonzero trace trν or the space of supertraces contains a degenerate nonzero supertrace strν and, as a consequence, the algebra ℋ has two-sided ideals: one consisting of all vectors in the kernel of the form or another consisting of all vectors in the kernel of the form . We noticed that if , where z ∈ ℤ\\(2m + 1)ℤ, then there exist both a degenerate trace and a degenerate supertrace on ℋ. Here we prove that the ideals determined by these degenerate forms coincide.