2022/04/21 by Damiano Rossi, Rossi, Damiano
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2204.10301
We work towards a version of generalized Harish-Chandra theory compatible with Clifford theory and with the action of automorphisms on irreducible characters. This provides a fundamental tool to verify the inductive conditions for the so-called local-global conjectures in representation theory of finite groups in the crucial case of groups of Lie type in non-defining characteristic. In particular, as shown by the author in an earier paper, this as a strong impact on the verification of the inductive condition for Dade's Conjecture. As a by-product, we also show how to extend the parametrization of generalized Harish-Chandra series given by Broué, Malle and Michel to the non-unipotent case by assuming maximal extendibility.