English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Let F be a non-archimedean local field, of characteristic 0. Let V be afinite dimensional vector space over F and q be a non-degenerate quadratic formon V. Denote d the dimension of V and G=SO(d) the special orthogonal group of(V,q). Let v_{0}\in V such that q(v_{0})\not=0, denote W the subspace of Vorthogonal to v_{0} and H=SO(d-1) the special orthogonal group of W. Let \pi,resp. \sigma, an admissible irreducible representation of G(F), resp. H(F).Denote m(\sigma,\pi) the dimension of the complex space Hom_{H(F)}(\pi_{|H(F)},\sigma). By a theorem of Aizenbud, Gourevitch, Rallis and Schiffmann, weknow that m(\sigma,\pi)=0 or 1. We define another term m_{geom}(\sigma,\pi).It's an explicit sum of integrals of functions that can be deduced from thecharacters of \sigma and \pi. Assume that \pi is supercuspidal. Then we provethe equality m(\sigma,\pi)=m_{geom}(\sigma,\pi). Now, let \Pi, resp. \Sigma, anL-packet of tempered representations of G(F), resp. H(F). We use thesophisticated notion of L-paquet due to Vogan: the representations in thepackets can be representations of inner forms of G(F), resp. H(F). We assumethat certain conjectural properties of tempered L-packets are true. Assume thatall elements of \Pi are supercuspidal. Then our integral formula implies theweak form of the Gross-Prasad conjecture: there exist a unique pair\sigma\times \pi\in \Sigma\times \Pi such that m(\sigma,\pi)=1.

Une formule int\'egrale reli\'ee \`a la conjecture locale de Gross-Prasad