Abstract
LetG(F q ) be a finite classical group whereq is odd and the centre ofG is connected. We show that there exists a set of irreducible characters ofG(F q ) such that the corresponding matrix of scalar products with the characters of Kawanakaâs generalized Gelfand-Graev representations is square unitriangular. This uses in an essential way Lusztigâs theory of character sheaves. As an application we prove that there exists an ordinary basic set of 2-modular Brauer characters and that the decomposition matrix of the principal 2-block ofG(F q ) has a lower unitriangular shape.
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