Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Residual automorphic forms and spherical unitary representations of
  exceptional groups   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 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 marking of a coadjoint nilpotent orbit of the Langlands dual Lie
algebra.

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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con