On the Schur indices of the irreducible characters of finite unitary groups (Q1583800)

The author investigates the Schur indices of the irreducible characters of the finite unitary groups \(U(n,q^2)\), where \(q\) is a power of a prime \(p\). It is known from earlier work of Gow and the author that these Schur indices will be at most \(2\), and that the local Schur indices will all be \(1\), except possibly at \(\infty\) and \(p\). In this paper, the author investigates conditions under which the Schur index of such a character is \(1\), and conditions under which the Schur index is \(2\). These conditions are sufficient to calculate the Schur indices of many irreducible characters of \(U(n,q^2)\), including all the irreducible characters in the case \(p=2\).