Semisimple symplectic characters of finite unitary groups

2009/04/11 by Vinroot, C. Ryan
#05E05 #20C33 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0904.1820

Abstract

Let G = \rm U(2m, \mathbb F_q²) be the finite unitary group, with q the power of an odd prime p. We prove that the number of irreducible complex characters of G with degree not divisible by p and with Frobenius-Schur indicator -1 is q^m-1. We also obtain a combinatorial formula for the value of any character of \rm U(n, \mathbb F_q²) at any central element, using the characteristic map of the finite unitary group.

Related

• Values of characters sums for finite unitary groups
• Real representations of finite symplectic groups over fields of\n characteristic two
• Low-dimensional complex characters of the symplectic and orthogonal groups
• q-deformed Character Theory for Infinite-Dimensional Symplectic and Orthogonal Groups
• Generating functions for real character degree sums of finite general linear and unitary groups