Work

Jordan correspondence and block distribution of characters

Year: 2025

Type: article

Abstract: We complete the determination of the ‐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 ‐block distribution for finite reductive groups whose ambient algebraic group defined in characteristic different from has connected centre. As a consequence, we derive a compatibility between ‐blocks, ‐Harish‐Chandra series and Jordan decomposition. Further, we apply our results to complete the proof of Robinson's conjecture on defects of characters.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70076

Authors: Radha Kessar, Gunter Malle

Institutions: University of Manchester, University of Kaiserslautern

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Isaac Newton Institute for Mathematical Sciences, Deutsche Forschungsgemeinschaft, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences