Jordan correspondence and block distribution of characters

Abstract

We complete the determination of the $\ell$-block distribution of characters for quasi-simple exceptional groups of Lie type up to some minor ambiguities relating to non-uniqueness of Jordan decomposition. For this, we first determine the $\ell$-block distribution for finite reductive groups whose ambient algebraic group defined in characteristic different from $\ell$ has connected centre. As a consequence, we derive a compatibility between $\ell$-blocks, $e$-Harish-Chandra series and Jordan decomposition. Further, we apply our results to complete the proof of Robinson's conjecture on defects of characters.