Let G = U(2m, Fq2) 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 qm-1. We also obtain a combinatorial formula for the value of any character of U(n, Fq2) at any central element, using the characteristic map of the finite unitary group.
Semisimple symplectic characters of finite unitary groups
Semisimple symplectic characters of finite unitary groups