Isolated blocks in finite classical groups, II

Abstract

The l-blocks of finite classical groups, where l is a prime not equal to the defining characteristic of the groups, are classified by l ′ -semisimple classes in the dual groups. The blocks corresponding to semisimple classes of elements with eigenvalues ±1 in the natural representations of the dual groups are called isolated blocks. These blocks were described in an earlier paper of the author for the groups Sp ( 2 n , q ) and SO ± ( 2 n , q ) ( q odd, l odd) via Lusztig induction. In this paper a combinatorial description of the isolated blocks of Sp ( 2 n , q ) and O ± ( 2 n , q ) ( q odd, l odd) in terms of Lusztig symbols is given for large q, using some results of Waldspurger.