Abstract

Let G be a connected reductive algebraic group defined over 𝔽_q, where q is a power of a prime p that is good for G. Let F be the Frobenius morphism associated with the 𝔽_q-structure on G and set G = G ^F, the fixed point subgroup of F. Let P be an F-stable parabolic subgroup of G and let U be the unipotent radical of P; set P = P ^F and U = U ^F. Let G _uni be the set of unipotent elements in G. In this note we show that the number of conjugacy classes of U in G _uni is given by a polynomial in q with integer coefficients.