On Theta Ranks of Irreducible Characters of a Finite Classical Group

2021/02/18 by Pan, Shu-Yen
#20C33 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2102.09220

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.

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