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Recently, G. Navarro introduced a new conjecture that unifies the AlperinWeight Conjecture and the Glauberman correspondence into a single statement. Inthis paper, we reduce this problem to simple groups and prove it for severalclasses of groups and blocks. Our reduction can be divided into two steps.First, we show that assuming the so-called Inductive (Blockwise) Alperin WeightCondition for finite simple groups, we obtain an analogous statement forarbitrary finite groups, that is, an automorphism-equivariant version of theAlperin Weight Conjecture inducing isomorphisms of modular character triples.Then, we show that the latter implies Navarro's conjecture for each finitegroup.

The Alperin Weight Conjecture and the Glauberman correspondence via character triples