Abstract
Abstract 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.
Published Version
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