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Low-dimensional representations of finite orthogonal groups

Part of: Representation theory of groups Linear algebraic groups and related topics

Published online by Cambridge University Press:  26 January 2021

KAY MAGAARD  and
GUNTER MALLE
KAY MAGAARD
Affiliation:
FB Mathematik, TU Kaiserslautern, Postfach 3049, 67653Kaiserslautern, Germany.
GUNTER MALLE*
Affiliation:
FB Mathematik, TU Kaiserslautern, Postfach 3049, 67653Kaiserslautern, Germany.
*
e-mail: malle@mathematik.uni-kl.de
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Abstract

We determine the smallest irreducible Brauer characters for finite quasi-simple orthogonal type groups in non-defining characteristic. Under some restrictions on the characteristic we also prove a gap result showing that the next larger irreducible Brauer characters have a degree roughly the square of those of the smallest non-trivial characters.

MSC classification

Primary: 20C33: Representations of finite groups of Lie type
Secondary: 20D06: Simple groups 20G40: Linear algebraic groups over finite fields
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 171 , Issue 3 , November 2021 , pp. 585 - 606
Copyright
© Cambridge Philosophical Society 2021

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