Une formule intégrale reliée à la conjecture locale de Gross–Prasad
By J. Waldspurger. Compositio Mathematica, 2009
98 citations recorded by the source corpus.
Abstract Let V be a vector space over a p-adic field F, of finite dimension, let q be a non-degenerate quadratic form over V and let D be a non-isotropic line in V. Denote by W the hyperplane orthogonal to D, and by G and H the special orthogonal groups of V and W. Let π, respectively σ, be an irreducible admissible representation of G(F) , respectively H(F) . The representation σ appears as a quotient of the restriction of π to H(F) with a certain multiplicity m(π,σ) . We know that m(π,σ)≤1 . We assume that π is supercuspidal. Then we prove a formula that computes m(π,σ) as an integral of functions deduced from the characters of π and σ. Let Π, respectively Σ, be an L-packet of tempered irreducible representations of G(F) , respectively H(F) . Here we use the sophisticated notion of L-packet due to Vogan and we assume some usual conjectural properties of those packets. A weak form of the local Gross–Prasad conjecture says that there exists a unique pair (π,σ)∈Π×Σ such that m(π,σ)=1 . Assuming that the elements of Π are supercuspidal, we prove this assertion.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8d1a3e92a737a2d713dbdea36f4225cbd944d731
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In Geometry and Topology
- W. Gan
- Atsushi Ichino
- Hiraku Atobe
- Wei Zhang
- Paul D. Nelson
- Shuichiro Takeda
- Ralf Schmidt
- Michael Rapoport
In Mathematical Physics
- W. Gan
- Atsushi Ichino
- Wei Zhang
- Hiraku Atobe
- Shuichiro Takeda
- Paul D. Nelson
- Michael Rapoport
- Ralf Schmidt
Citations in the corpus
- The Gross–Prasad conjecture and local theta correspondence (2014, background): “In a stunning series of papers [20], [21], [22], [23], Waldspurger has established the Bessel case of the GP conjecture for tempered L-parameters φ in the case of special orthogonal groups; the case of general generic L-parameters is then dealt with by Mœglin-Waldspurger [13].”