A local-global principle for unipotent characters

<p dir="ltr">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 <b>A</b>, <b>B</b> and <b>C</b>. In particular, this gives a precise formula for counting the number of unipotent characters of each defect <i>d</i> in any Brauer ℓ -block <b><i>B</i></b> in terms of local invariants associated to <i>e</i>-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.</p>