Eigenspaces and Regular Elements

Abstract

Let $\phi \,\, \in \,\, N_{\rm GL(V)}(G)$ with finite order. Let $(d_1, \zeta_1), (d_2, \zeta_2), ... , (d_r, \zeta_r)$ be the family of generalized characteristic degrees of (G, φ): there exists an algebraic basis $(u_i)_{1 \leq i \leq r}$ of R such that, for $1 \leq i \leq r$ we have $\deg u_i = d_i\,\, {\rm and}\,\, \phi (u_i) = \zeta_i u_i$.