On a Zelevinsky Theorem and the Schur Indices of the Finite Unitary Groups

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J. Math. Sci. Univ. Tokyo
Vol. 4 (1997), No. 2, Page 417--433.

Ohmori, Zyozyu
On a Zelevinsky Theorem and the Schur Indices of the Finite Unitary Groups
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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

$Î»$ of

$U$ such that

$(Î»^G, Ï)_G=1$ . 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

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