Genericity and contragredience in the local Langlands correspondence
arXiv:1204.0132
Abstract
We prove the recent conjectures of Adams-Vogan and D. Prasad on the behavior of the local Langlands correspondence with respect to taking the contragredient of a representation. The proof holds for tempered representations of quasi-split real K-groups and quasi-split p-adic classical groups (in the sense of Arthur). We also prove a formula for the behavior of the local Langlands correspondence for these groups with respect to changes of the Whittaker data.
Minor changes to the introduction and references to place the paper in the proper context. Corollary 4.10 added. An inaccuracy in the treatment of even orthogonal groups fixed