Isotypies for the quasisimple groups with exceptional Schur multiplier

Abstract

Let [Formula: see text] be a block with abelian defect group [Formula: see text] of a quasisimple group [Formula: see text], such that [Formula: see text] has exceptional Schur multiplier. We show that, [Formula: see text] is isotypic to its Brauer correspondent in [Formula: see text] in the sense of Broué. The proof uses methods from a previous paper [B. Sambale, Broué’s isotypy conjecture for the sporadic groups and their covers and automorphism groups, Internat. J. Algebra Comput. 25 (2015) 951–976], and relies ultimately on computer calculations. Moreover, we verify the Alperin–McKay conjecture for all blocks of [Formula: see text].