Damiano Rossi

• 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 A, B and C. In particular, this gives a precise formula for counting the number of unipotent characters of each defect d in any Brauer l-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.