On Arthur's Φ-Function

2005/03/24 by Steven Spallone, Spallone, Steven
Mathematics · #22E47 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:22E47

paper · pdf · doi:10.48550/arxiv.math/0503524

11 pages

arxiv created 2005/03/24 · arxiv updated 2009/12/01

Abstract

Write Θ^E for the stable character associated to a finite dimensional representation E of a connected real reductive group G. Let M be the centralizer of a maximal torus T, and denote by Φ_M(\gm,Θ^E) Arthur's extension of |D_M^G(\gm)|^\half Θ^E(\gm) to T(\R). In this paper we give a simple explicit expression for Φ_M(\gm,Θ^E), when \gm is elliptic in G.

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