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

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For each complex number ν, an associative symplectic reflection algebra ℋ := H1,ν (I2(2m+1)), based on the group generated by root system I2(2m+1), has an m-dimensional space of traces and an (m+1)-dimensional space of supertraces. A (super)trace sp is said to be degenerate if the corresponding bilinear (super)symmetric form Bsp(x,y) = sp(xy) is degenerate. We find all values of the parameter ν for which either the space of traces contains a degenerate nonzero trace or the space of supertraces contains a degenerate nonzero supertrace and, as a consequence, the algebra ℋ has a two-sided ideal of null-vectors. The analogous results for the case \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${H_{1,{v_1},{v_2}}}({I_2}(2m))$$\\end{document} are also presented.