Geodesic
A local-global principle for unipotent characters
Forum of Mathematics, Sigma, Tome 12 (2024)

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We obtain an adaptation of Dade’s Conjecture and Späth’s Character Triple Conjecture to unipotent characters of simple, simply connected finite reductive groups of type $\mathbf {A}$, $\mathbf {B}$ and $\mathbf {C}$. 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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     title = {A local-global principle for unipotent characters},
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Damiano Rossi. A local-global principle for unipotent characters. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.78

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