Invariant theory and eigenspaces for unitary reflection groups. (Q1408169)

Let \(G\) be a finite group generated by pseudo-reflections in a complex vector space \(V\). The ring \(S^G\) of polynomial invariants is free. Let \(f_1,\dots,f_\ell\) be homogeneous free generators for \(S^G\), then the degrees \(d_i=\deg f_i\) are determined by \(G\). A theorem of \textit{G. I. Lehrer} and \textit{T. A. Springer} [Can. J. Math. 51, No. 5, 1175-1193 (1999; Zbl 0958.51017)] provides a criterion for an integer to be regular for \(G\), involving the \(d_i\) above. The authors of the present paper generalize this theorem.