On Theta Ranks of Irreducible Characters of a Finite Classical Group

Abstract

In this paper, we interpret the theta rank of an irreducible character of a finite classical group in terms of the data from the Lusztig classification. Then we prove the following two results: (1) the agreement of the $U$-rank and the theta rank for any irreducible character of low Theta rank; (2) the agreement of the parabolic asymptotic rank and the theta rank for any irreducible character.