Ideals generated by traces or by supertraces in the symplectic reflection algebra H1, ν (I2(2m + 1))

For each complex number $\nu$, an associative symplectic reflection algebra $\mathcal H:= H_{1,\nu}(I_2(2m+1))$, based on the group generated by root system $I_2(2m+1)$, has $m$-dimensional space of traces and $(m+1)$-dimensional supertraces. A (super)trace $sp$ is said to be degenerate if corresponding bilinear (super)symmetric form $B_{sp}(x,y)=sp(xy)$ degenerate. We find all values parameter $\nu$ for which either contains a nonzero trace or supertraces supertrace and, as consequence, H$ two-sided ideal null-vectors. The analogous results $H_{1,\nu_1, \nu_2}(I_2(2m))$ are also presented.