Wavefront Sets of Unipotent Representations of Reductive p-adic Groups I

2021/12/29 by Ciubotaru, Dan, Mason-Brown, Lucas, Okada, Emile
#11F70 #22E50 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2112.14354

Abstract

The wavefront set is a fundamental invariant arising from the Harish-Chandra-Howe local character expansion of an admissible representation. We prove a precise formula for the wavefront set of an irreducible Iwahori-spherical representation with `real infinitesimal character' and determine a lower bound for this invariant in terms of the Deligne-Langlands-Lusztig parameters. In particular, for the Iwahori-spherical representations with real infinitesimal character, we deduce that the algebraic wavefront set is a singleton, as conjectured by Moeglin and Waldspurger. As a corollary, we obtain an explicit description of the wavefront set of an irreducible spherical representation with real Satake parameter.

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