Abstract:
One of the most important problem in modular representation theory of finite groups is the Alperin weight conjecture. This conjecture has been reduced to simple groups by Navarro-Tiep and Späth; to prove the conjecture, it suffices to verify the so-called inductive condition for all finite non-abelian simple groups. Using a criterion given by Brough and Späth, the inductive condition is verified for simple groups of Lie type B under the unitriangularity assumption of the decomposition matrices. Joint work with Conghui Li and Jiping Zhang.