Local Theta correspondence of Tempered Representations and Langlands parameters

Abstract

In this paper, we give an explicit determination of the theta lifting for symplectic-orthogonal and unitary dual pairs over a nonarchimedean field $F$ of characteristic $0$. We determine when theta lifts of tempered representations are nonzero, and determine the theta lifts in terms of the local Langlands correspondence.

45 pages

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• Simple supercuspidal L-packets of quasi-split classical groups
• Unitary Friedberg-Jacquet periods
• The Prasad conjectures for $\mathrm{GS}{\mathrm{p}}_4$ and $\mathrm{PGS}{\mathrm{p}}_4$
• Theta lifting for discrete series representations of real unitary groups
• Local Langlands Correspondence for Unitary Groups via Theta Lifts
• The local Gan-Gross-Prasad conjecture for $U(3)\times U(2)$ : the non-generic case
• The automorphic discrete spectrum of ${\mathrm{Mp}}_4$
• Correspondences between affine Hecke algebras and applications
• Theta lifting for tempered representations of real unitary groups
• Theta correspondence for symplectic-orthogonal and metaplectic-orthogonal p-adic dual pairs
• Theta lifts of generic representations for dual pairs $({\mathrm{Sp}}_{2n},\mathrm{O}(V))$
• Theta lifts and distinction for regular supercuspidal representations
• On the non-vanishing of theta liftings of tempered representations of U(p,q)