A formula for the number of semi-simple conjugacy classes in the arithmetic subgroups
It would be appropriate to quote some sentences from the paper with slight modifications. - The purpose of this note is to present a general formula for the number of conjugacy classes in the arithmetic subgroups of a reductive algebraic group G defined over an algebraic number field k, of those elements which are contained in a semi-simple conjugacy class of \(G_ k\). With the knowledge of the parametrization of \(G_ k\)- conjugacy classes developed in the relevant papers, the formula obtained in this paper gives us an effective procedure to count explicitly the number of semi-simple conjugacy classes with given characteristic polynomials in a wide class of arithmetic subgroups of the classical groups.
scientific article; zbMATH DE number 3922759
scientific article