IRREDUCIBLE CHARACTERS FOR ALGEBRAIC GROUPS IN CHARACTERISTIC THREE

Abstract

All irreducible characters for the special orthogonal group SO(7, K) and the symplectic group Sp(6, K) over an algebraically closed field K of characteristic 3 are determined, and the Cartan invariant matrix for the finite group SO(7, 3) is also calculated in this note.

Keywords:

• Irreducible character
• Semisimple algebraic group
• Cartan invariant matrix

ACKNOWLEDGMENTS

Supported in part by the NNSFC grant 19771061. Part of this note was done during the period that the first named author visited Bielefeld University in 1999. He is grateful to the Sonderforschungsbereich 343 at Bielefeld University for its financial support.