2021/09/06 by Jean-Loup Waldspurger, Waldspurger, Jean-Loup
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2109.02373
openalex publication_date 2021/09/06 · openalex created_date 2021/09/13 · openalex updated_date 2026/08/01
Let G be a connected reductive group defined over a non-archimedean local field of characteristic 0. We assume G is quasi-split, adjoint and absolutly simple. Let g be the Lie algebra of G. We consider the space of the invariant distributions on g(F), which are stable and supported by the set of nilpotent elements of g(F). Magdy Assem has stated several conjectures which describe this space. We prove some of these conjectures, assuming that the residual characteristic of F is ''very large'' relatively to G.