On the conjugacy classes in the orthogonal and symplectic groups over algebraically closed fields

Abstract

Listen

Translate article

Let F be an algebraically closed field. Let V be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form B over F . Suppose the characteristic of F is sufficiently large, i.e. either zero or greater than the dimension of V . Let I ( V , B ) denote the group of isometries. Using the Jacobson–Morozov lemma we give a new and simple proof of the fact that two elements in I ( V , B ) are conjugate if and only if they have the same elementary divisors.