2009/10/13 by Jean-Loup Waldspurger, Waldspurger, Jean-Loup
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.0910.2294
openalex publication_date 2009/10/13 · arxiv created 2012/05/05 · arxiv updated 2012/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let d and m be two natural numbers of distinct parities. Let π be an admissible irreducible tempered representation of GL(d,F), where F is a p-adic field. We assume that π is self-dual. Then we can extend π as a representation π of a non-connected group GL(d,F)\rtimes \1,θ\. Let ρ be a representation of GL(m,F). We assume that it has similar properties as π. Jacquet, Piatetski-Shapiro and Shalika have defined the factor ε(s,π×ρ,ψ). We prove that we can compute ε(1/2,π×ρ,ψ) by an integral formula where occur the characters of π and ρ. It's similar to the formula which, for special orthogonal groups, computes the multiplicities appearing in the local Gross-Prasad conjecture.