Genericity and contragredience in the local Langlands correspondence

By Tasho Kaletha. 2012

57 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/900c7a4d2e32dbf7ae0a203c709734a1ff34489f

Citations in the corpus

• Local theta correspondence of tempered representations and Langlands parameters (2016, unknown): “f E= F and ǫ= −1. Here, in the first case, we fix δ∈Esuch that trE/F(δ) = 0 and put ψE(x) = ψ(1 2trE/F(δx)) for x∈E. The L-parameter for the contragredient representation π∨ of πis described by Kaletha [Ka]. Proposition B.3 ([Ka, Theorem 4.9]). Let π ∈Irr(H(Vm)) with L-parameter (φπ,ηπ). We denote the”