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Stable distributions and nilpotent orbital integrals

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arxiv 2109.02373 v3 pith:IRQI7WGR submitted 2021-09-06 math.RT

Jean-Loup Waldspurger (IMJ-PRG) This is my paper · ORCID
classification math.RT
keywords characteristicconjecturesdistributionsnilpotentspacestableabsolutlyadjoint
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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.

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Cited by 1 Pith paper

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  1. Germ expansion for SL(2) in arbitrary characteristics

    math.RT 2025-07 conditional novelty 4.0 of 10

    For SL(2) over local fields of any characteristic, including p=2 where Shalika's expansion fails, the paper proves an endoscopic germ expansion for orbital integrals near the center and states a conjecture for arbitra...

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