Certain Unitary Langlands-Vogan Parameters for Special Orthogonal Groups I

Details Certain Unitary Langlands-Vogan Parameters for Special Orthogonal Groups I Certain Unitary Langlands-Vogan Parameters for Special Orthogonal Groups I

2011-01-03

arxiv.org/abs/1101.0441v1

Mathematics

Representation Theory

39 Pages

Scientific paper

A Langlands parameter, in the Langlands dual group, can be decomposed into a product of a tempered parameter and a positive quasi-character. Fixing a tempered parameter, Arthur conjectured that positive quasi-characters corresponding to certain weighted Dynkin diagrams for the centralizer of the tempered parameter will yield unitary representations. In this paper, we treat one basic case in Arthur's conjecture for the special orthogonal groups. We establish the unitarity for a class of Langlands-Vogan parameters in Arthur's packet.

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