Residual automorphic forms and spherical unitary representations of exceptional groups

2012/05/02 by Stephen D. Miller, Miller, Stephen D.
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1205.0426

8 pages. The computational data and programs can be found at http://www.math.rutgers.edu/~sdmiller/L2

arxiv created 2012/05/02 · arxiv updated 2012/05/03

Abstract

Arthur has conjectured that the unitarity of a number of representations can be shown by finding appropriate automorphic realizations. This has been verified for classical groups by Moeglin and for the exceptional Chevalley group G₂ by Kim. In this paper we extend their results on spherical representations to the remaining exceptional groups E₆, E₇, E₈, and F₄. In particular we prove Arthur's conjecture that the spherical constituent of an unramified principal series of a Chevalley group over any local field of characteristic zero is unitarizable if its Langlands parameter coincides with half the marking of a coadjoint nilpotent orbit of the Langlands dual Lie algebra.

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