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arXiv · 2301.05151

A local-global principle for unipotent characters

Damiano Rossi
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Abstract

We obtain an adaptation of Dade's Conjecture and Sp\"ath's Character Triple Conjecture to unipotent characters of simple, simply connected finite reductive groups of type $\bf{A}$, $\bf{B}$ and $\bf{C}$. In particular, this gives a precise formula for counting the number of unipotent characters of each defect $d$ in any Brauer $\ell$-block $B$ in terms of local invariants associated to $e$-local structures. This provides a geometric version of the local-global principle in representation theory of finite groups. A key ingredient in our proof is the construction of certain parametrisations of unipotent generalised Harish-Chandra series that are compatible with isomorphisms of character triples.

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Damiano Rossi. 2023-01-12. A local-global principle for unipotent characters. https://doi.org/10.1017/fms.2024.78

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