Related papers: Fourier-Jacobi models for real symplectic-metaplec…

We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet--Rallis relative trace formula, we complete the proof of the global Gan--Gross--Prasad conjecture and its…

We study Whittaker vectors (and Jacquet integrals) in the generalized principal series for a real reductive group. A functional equation for them is obtained. This allows to establish uniform estimates for their holomorphic extensions with…

Lapid and Mao conjectured Ichino-Ikeda type formula of Whittaker periods for any quasi-split reductive groups and metaplectic groups. In this paper, we prove this formula for any irreducible cuspidal globally generic automorphic…

The local non-tempered Gan-Gross-Prasad conjecture suggests that, for a pair of irreducible Arthur type representations of two successive general linear groups, they have a non-zero Rankin-Selberg period if and only if they are "relevant".…

We extend the notion of generalized Whittaker models by allowing them to be built upon smooth irreducible representations of unipotent subgroups of a $p$-adic reductive group that are not necessarily characters, nor induced from Weil…

Following Arthur's study of the representations of the orthogonal and symplectic groups, we prove many cases of both the local and global Arthur conjectures for tempered representations of the unitary group. This completes the proof of…

In this paper we prove that Ext-analogues of Gan--Gross--Prasad models vanish for tempered representations, as conjectured by D. Prasad. In particular, this implies a conjectural Euler--Poincar\'e characteristic formula for…

In \cite{JZ1}, D. Jiang and L. Zhang proposed a conjecture which related the wavefront sets and the descent method in the local fields case. Recently, in \cite{JLZ}, they and D. Liu define the arithmetic wavefront set of certain irreducible…

We give a general proof of Shahidi's tempered L-function conjecture, which has previously been known in all but one case. One of the consequences is the standard modules conjecture for p-adic groups, which means that the Langlands quotient…

The Local Converse Problem is to determine how the family of the local gamma factors $\gamma(s,\pi\times\tau,\psi)$ characterizes the isomorphism class of an irreducible admissible generic representation $\pi$ of $\mathrm{GL}_n(F)$, with…

We prove in the case of equal characteristic a fundamental lemma conjectured by Jacquet and Mao for the metaplectic group. We use the arguments of Bao Ch\^au Ng\^o for Jacquet-Ye's fundamental lemma and a geometric study of the metaplectic…

In a recent paper, Gabriel Navarro and Pham Huu Tiep show that the so-called Alperin Weight Conjecture can be verified via the Classification of the Finite Simple Groups, provided any simple group fulfills a very precise list of conditions.…

In this work we introduce a new algebra of tempered generalized functions. The tempered distributions are embedded in this algebra via their Hermite expansions. The Fourier transform is naturally extended to this algebra in such a way that…

We prove a restricted projection theorem for Borel subsets of $\mathbb{Q}_p^n$ in the regime $p>n$. This generalizes results of Gan-Guo-Wang in the real setting. Our result is effective in the sense that explicit constants are obtained for…

In this paper, we form a conjecture about the multiplicities of all the strongly tempered spherical varieties without Type N root for tempered representations. This generalizes the epsilon dichotomy conjectures of Gan-Gross-Prasad and…

We give a new local proof of the Breuil-M\'ezard conjecture in the case of a reducible representation of the absolute Galois group of $\mathbb{Q}_p$, $p>2$, that has scalar semi-simplification, via a formalism of Pa\v{s}k\=unas.

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…

Let $G$ be a simple group over a global function field $K$, and let $\pi$ be a cuspidal automorphic representation of $G$. Suppose $K$ has two places $u$ and $v$ (satisfying a mild restriction on the residue field cardinality), at which the…

Using a relative trace formula approach, we prove the twisted global Gan-Gross-Prasad conjecture for $\operatorname{U}(V) \subseteq \operatorname{GL}(V)$, as well as its refinement, under some unramifiedness assumptions and local conditions…

We give the generalized Atiyah-Schmid formula for projective tempered representations. Then we prove the Atiyah-Schmid formula for arithmetic subgroups of real reductive groups.