On conjugacy classes of elements of finite order in complex semisimple lie groups

AbstractThe main theme of this paper is the study of the number, v(G,k), of conjugacy clases of a complex semisimple group G which consist of elements whose orders divide k. We define an involution ∨ on the set of isomorphism classes of such groups and show that ν(G∨,k) = ν(G,k). Explicit formulas for ν(G,k) are obtained for all simply connected or adjoint groups, as well as for all groups of type Al. We obtain also some new partition identities which may be of interest to number-theorists