Related papers: Theta Correspondence and Arthur packets

Arthur packets have been defined for pure real forms of symplectic and special orthogonal groups following two different approaches. The first approach, due to Arthur, Moeglin and Renard uses harmonic analysis. The second approach, due to…

In this paper, we give an algorithm to determine all local A-packets containing a given irreducible representation of a p-adic classical group. Especially, we can determine whether a given irreducible representation is of Arthur type or…

This paper serves as an attempt towards the Jiang conjecture on the upper bound nilpotent orbits in the wavefront sets of representations in local Arthur packets of quasi-split classical groups, which is a natural generalization of the…

We construct local Arthur packets associated with a dihedral long root $A$-parameter of a split reductive group of type $G_2$ over a nonarchimedian local field of characteristic zero. The construction relies on an exceptional correspondence…

We establish the endoscopic character identity for bounded $A$-packets of non-quasisplit even special orthogonal groups, with respect to elliptic endoscopic triples. The proof reduces the non-quasisplit case to the quasisplit case and the…

Weak Arthur packets have long been instrumental in the study of the unitary dual and automorphic spectrum of reductive Lie groups, and were recently introduced in the p-adic setting by Ciubotaru - Mason-Brown - Okada. For split odd…

In this paper, we prove the closure ordering conjecture on the local $L$-parameters of representations in local Arthur packets of $\mathrm{G}_n=\mathrm{Sp}_{2n}, \mathrm{SO}_{2n+1}$ over a non-Archimedean local field of characteristic zero.…

Cuspidal automorphic representations $\tau$ of $\mathrm{PGL}_2$ correspond to global long root $A$-parameters for $\mathsf{G}_2$. Using an exceptional theta lift between $\mathrm{PU}_3$ and $\mathsf{G}_2$, we construct the associated global…

We give an explicit construction of Arthur packets for real unitary groups by cohomological and parabolic induction and following an idea communicated to us by P. Trapa, we show that they satisfy the multiplicity one property. In…

Mok and Moeglin-Renard have defined Arthur packets for unitary groups. Their definitions follow Arthur's work on classical groups and rely on harmonic analysis. For real groups there is an alternative definition of Arthur packets due to…

This is a report on the progress made on a conjecture of Jiang on the upper bound nilpotent orbits in the wave front sets of representations in local Arthur packets of classical groups, which is a natural generalization of the Shahidi…

By using results on poles of $L$-functions and theta correspondence, we give a bound on $b$ for $(\chi,b)$-factors of the global Arthur parameter of a cuspidal automorphic representation $\pi$ of a classical group or a metaplectic group…

Let $k$ be a $p$-adic field and let $\mathbf{G}(k)$ be the $k$-points of a connected reductive group, inner to split. The set of Aubert-Zelevinsky duals of the constituents of a tempered L-packet form an Arthur packet for $\mathbf{G}(k)$.…

This paper begins the project of defining Arthur packets of all unipotent representations for the $p$-adic exceptional group $G_2$. Here we treat the most interesting case by defining and computing Arthur packets with component group $S_3$.…

We prove a conjecture of the first-named author ([J14]) on the upper bound Fourier coefficients of automorphic forms in Arthur packets of all classical groups over any number field. This conjecture generalizes the global version of the…

We give upper bounds on limit multiplicities of certain non-tempered representations of unitary groups $U(a,b)$. These include some cohomological representations, and we give applications to the growth of cohomology of cocompact arithmetic…

We study the validity of the local theta correspondence over a non-archimedean local field in the context of modular representation theory \textit{i.e.} for representations with coefficient fields of positive characteristic. For a…

This article is part of a project which consists of investigating Arthur packets for real classical groups. Our goal is to give an explicit description of these packets and to establish the multiplicity one property (which is known to hold…

In the paper we begin to explore relation between the question of unitarizability of classical p-adic groups, and Arthur packets.

In this paper we first construct natural filtrations on the full theta lifts for any real reductive dual pairs. We will use these filtrations to calculate the associated cycles and therefore the associated varieties of Harish-Chandra…