oalib
Search Results: 1 - 10 of 100 matches for " "
All listed articles are free for downloading (OA Articles)
Page 1 /100
Display every page Item
A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the archimedean case  [PDF]
Rapha?l Beuzart-Plessis
Mathematics , 2015,
Abstract: In this paper, we prove, following earlier work of Waldspurger ([Wa1], [Wa4]), a sort of local relative trace formula which is related to the local Gan-Gross-Prasad conjecture for unitary groups over a local field $F$ of characteristic zero. As a consequence, we obtain a geometric formula for certain multiplicities $m(\pi)$ appearing in this conjecture and deduce from it a weak form of the local Gan-Gross-Prasad conjecture (multiplicity one in tempered L-packets). These results were already known over $p$-adic fields and thus are only new when $F=\mathbb{R}$.
A proof of the refined Gan--Gross--Prasad conjecture for non-endoscopic Yoshida lifts  [PDF]
Andrew Corbett
Mathematics , 2015,
Abstract: We prove a precise formula relating the Bessel period of certain automorphic forms on ${\rm GSp}_{4}(\mathbb{A}_{F})$ to a central $L$-value. This is a special case of the refined Gan--Gross--Prasad conjecture for the groups $({\rm SO}_{5},{\rm SO}_{2})$ as set out by Ichino--Ikeda and Liu. This conjecture is deep and hard to prove in full generality; in this paper we succeed in proving the conjecture for forms lifted, via automorphic induction, from ${\rm GL}_{2}(\mathbb{A}_{E})$ where $E$ is a quadratic extension of $F$. The case where $E=F\times F$ has been previously dealt with by Liu.
A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the archimedean case  [PDF]
Rapha?l Beuzart-Plessis
Mathematics , 2015,
Abstract: In this paper, we prove, following earlier work of Waldspurger ([Wa1], [Wa4]), a sort of local relative trace formula which is related to the local Gan-Gross-Prasad conjecture for unitary groups over a local field $F$ of characteristic zero. As a consequence, we obtain a geometric formula for certain multiplicities $m(\pi)$ appearing in this conjecture and deduce from it a multiplicity one result in tempered L-packets. These results were already known over $p$-adic fields ([Beu1]) and thus are only new when $F=\mathbb{R}$.
The Gross-Prasad conjecture and local theta correspondence  [PDF]
Wee Teck Gan,Atsushi Ichino
Mathematics , 2014,
Abstract: We establish the Fourier-Jacobi case of the local Gross-Prasad conjecture for unitary groups, by using local theta correspondence to relate the Fourier-Jacobi case with the Bessel case established by Beuzart-Plessis. To achieve this, we prove two conjectures of D. Prasad on the precise description of the local theta correspondence for (almost) equal rank unitary dual pairs in terms of the local Langlands correspondence.
Endoscopie et conjecture raffinée de Gan-Gross-Prasad pour les groupes unitaires  [PDF]
Rapha?l Beuzart-Plessis
Mathematics , 2012, DOI: 10.1112/S0010437X14007891
Abstract: Under endoscopic assumptions about $L$-packets of unitary groups, we prove the local Gan-Gross-Prasad conjecture for tempered representations of unitary groups over $p$-adic fields. Roughly, this conjecture says that branching laws for $U(n-1)\subset U(n)$ can be computed using epsilon factors.
Gan-Gross-Prasad Conjecture for U(p,q)  [PDF]
Hongyu He
Mathematics , 2015,
Abstract: In this paper, we give a proof of the Gan-Gross-Prasad conjecture for discrete series of U(p,q).
On the global Gross-Prasad conjecture for Yoshida liftings  [PDF]
Siegfried B?cherer,Masaaki Furusawa,Rainer Schulze-Pillot
Mathematics , 2002,
Abstract: We restrict a Siegel modular cusp form of degree 2 and square free level that is a Yoshida lifting (a lifting from the orthogonal group of a definite quaternion algebra) to the embedded product of two half planes and compute the Petersson product against the product of two elliptic cuspidal Hecke eigenforms. The square of this integral can be explicitly expressed in terms of the central critical value of an L-function attached to the situation. The result is related to a conjecture of Gross and Prasad about restrictions of automorphic representations of special orthogonal groups.
The local theta correspondence and the local Gan-Gross-Prasad conjecture for the symplectic-metaplectic case  [PDF]
Hiraku Atobe
Mathematics , 2015,
Abstract: We prove the local Gan-Gross-Prasad conjecture for the symplectic-metaplectic case under some assumptions. This is the last case of the local Gan-Gross-Prasad conjectures. We also prove two of Prasad's conjectures on the local theta correspondence in the almost equal rank case.
The local Gan-Gross-Prasad conjecture for $U(3) \times U(2)$ : the non-generic case  [PDF]
Jaeho Haan
Mathematics , 2015,
Abstract: In this paper, we investigate the local Gan-Gross-Prasad conjecture for some pair of representations of $U(3)\times U(2)$ involving a non-generic representation. For a pair of generic $L$-parameters of $(U(n),U(n-1))$, it is known that there is a unique pair of representations in their associateed Vogan $L$-packets which produces the unique Bessel model of these $L$-parameters. We showed that this is not ture for some pair of $L$-parameters involving a non-generic one.\\ On the other hand, we give the precise local theta correspondence for $(U(1),U(3))$ not at the level of $L$-parameters but of individual representations in the framework of the local Langlands correspondence for unitary group. As an applicaiton of these results, we prove an analog of Ichino-Ikeda conejcture for some non-tempered case.
La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes unitaires  [PDF]
Rapha?l Beuzart-Plessis
Mathematics , 2012,
Abstract: Let $E/F$ be a quadratic extension of non-archimedean local fields of characteristic 0 and let $G=U(n)$, $H=U(m)$ be unitary groups of hermitian spaces $V$ and $W$. Assume that $V$ contains $W$ and that the orthogonal complement of $W$ is a quasisplit hermitian space (i.e. whose unitary group is quasisplit over $F$). Let $\pi$ and $\sigma$ be smooth irreducible representations of $G(F)$ and $H(F)$ respectively. Then Gan, Gross and Prasad have defined a multiplicity $m(\pi,\sigma)$ which for $m=n-1$ is just the dimension of $Hom_{H(F)}(\pi,\sigma)$. For $\pi$ and $\sigma$ tempered, we state and prove an integral formula for this multiplicity. As a consequence, assuming some expected properties of tempered $L$-packets, we prove a part of the local Gross-Prasad conjecture for tempered representations of unitary groups. This article represents a straight continuation of recent papers of Waldspurger dealing with special orthogonal groups.
Page 1 /100
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.