On the computation of conjugacy classes of Chevalley groups
Let \(G\) be a connected reductive algebraic group defined over a Galois field \(F_q\) with corresponding Frobenius endomorphism \(F\) and a finite group \(G^F\) of \(F\)-fixed points. Two semisimple conjugacy classes \([s_1]\) and \([s_2]\) of \(G^F\) are called of the same genus if the centralizers \(C_G(s_1)\) and \(C_G(s_2)\) are conjugate under \(G^F\). An equivalence class is called a genus number. In this paper an algorithm is given to determine the number of semisimple conjugacy classes for a given centralizer type for the Chevalley groups \(\text{SL}_n(q)\) and \(\text{SU}_n(q)\). The authors determine the exact number of regular semisimple classes of these groups. They use Jordan decomposition to summarize results pertaining to the generic class number of exceptional Chevalley groups of adjoint type.
scientific article; zbMATH DE number 878205
scientific article