Arthur's infinitesimal-character conjecture for congruence spectra

Let GG be a semisimple algebraic group over Q{\mathbb Q}, let Γ\Gamma be a congruence subgroup, and let π\pi be an irreducible representation of GG occurring weakly in L2(Γ\G)L^2(\Gamma\backslash G). An Arthur parameter is a parameter φψ\varphi_{\psi} arising from an Arthur parameter ψ\psi. Arthur's infinitesimal-character conjecture. The infinitesimal character of π\pi is associated with an Arthur parameter φψ\varphi_{\psi}. This is a deliberately weak formulation of Arthur's conjectures concerning the partition of the automorphic dual into finite Arthur packets; the source gives no resolution of this assertion.

Sources & referencesView supporting material

Primary source

N. Bergeron, “Représentations cohomologiques isolées, applications cohomologiques”, arXiv:math/0511689 (2005).

Additional references

2 papers in this index state this conjecture (2004–2005). The statement above is taken from the most recent of them; the others are arXiv:math/0411385.

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