Residual automorphic forms and spherical unitary representations of exceptional groups

• Autores: Stephen D. Miller
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 177, Nº 3, 2013, págs. 1169-1179
• Idioma: inglés
• DOI: 10.4007/annals.2013.177.3.9
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• Resumen

  • 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 M\oe glin and for the exceptional Chevalley group G 2 by Kim. In this paper we extend their results on spherical representations to the remaining exceptional groups E 6 , E 7 , E 8 , and F 4 . 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 weighted marking of a coadjoint nilpotent orbit of the Langlands dual Lie algebra