Genericity and contragredience in the local Langlands correspondence

Details Genericity and contragredience in the local Langlands correspondence Genericity and contragredience in the local Langlands correspondence

2012-03-31

arxiv.org/abs/1204.0132v1

Mathematics

Representation Theory

20 pages, no figures

Scientific paper

Recently Adams and Vogan made a conjecture about the behavior of the local Langlands correspondence with respect to taking the contragredient of a representation. We prove this conjecture for the tempered L-packets of quasi-split classical p-adic groups constructed by Arthur. More precisely, we formulate a slight generalization of their conjecture and prove it for tempered representations of quasi-split real K-groups and quasi-split symplectic and special orthogonal p-adic groups. We also provide a formula for the behavior of the local Langlands correspondence with respect to changes of the Whittaker data.

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