2012/12/05 by Raphaël Beuzart-Plessis, Beuzart-Plessis, Raphaël
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Finite Group Theory Research #math.NT #math.RT
paper · pdf · doi:10.48550/arxiv.1212.1082
58p
arxiv created 2012/12/05 · arxiv updated 2012/12/06
Let E/F be a quadratic extension of p-adic fields and let d, m be nonnegative integers of distinct parities. Fix admissible irreducible tempered representations π and σ of GLd(E) and GLm(E) respectively. We assume that π and σ are conjugate-dual. That is to say π≃ π\vee,c and σ≃ σ\vee,c) where c is the non trivial F-automorphism of E. This implies, we can extend π to an unitary representation π of a nonconnected group GLd(E)\rtimes 1,θ. Define σ the same way. We state and prove an integral formula for ε(1/2,π× σ,ψE) involving the characters of π and σ. This formula is related to the local Gan-Gross-Prasad conjecture for unitary groups.