Semisimple symplectic characters of finite unitary groups

Details Semisimple symplectic characters of finite unitary groups Semisimple symplectic characters of finite unitary groups

2009-04-11

arxiv.org/abs/0904.1820v1

Mathematics

Representation Theory

20 pages

Scientific paper

Let $G = {\rm U}(2m, {\mathbb F}_{q^2})$ 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 ${\rm U}(n, {\mathbb F}_{q^2})$ at any central element, using the characteristic map of the finite unitary group.

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