On a Zelevinsky Theorem and the Schur Indices of the Finite Unitary Groups
Vol. 4 (1997), No. 2, Page 417--433.
Ohmori, Zyozyu
On a Zelevinsky Theorem and the Schur Indices of the Finite Unitary Groups
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
Let $G$ be the finite unitary group $U_n(\hbox{\tenbx F}_q)$ over a finite field $\hbox{\tenbx F}_q$ of characteristic $p$. Let $U$ be a Sylow $p$-subgroup of $G$. We prove that, for any irreducible character $Ï$ of $G$ that is contained in a certain class, there is a linear character $λ$ of $U$ such that $(λ^G, Ï)_G=1$. As an application, we shall determine the local Schur indices of an irreducible character of $G$ which belongs to such class.
Mathematics Subject Classification (1991): 20G05
Mathematical Reviews Number: MR1466354
Received: 1996-09-25
