Related papers: Paquets d'Arthur des groupes classiques et unitair…

Let $F$ be a $p$-adic field, and let $G$ be either the split special orthogonal group $\mathrm{SO}_{2n+1}(F)$ or the symplectic group $\mathrm{Sp}_{2n}(F)$, with $n \geq 0$. We prove that a smooth irreducible representation of good parity…

In [Ar13], Arthur classifies the automorphic discrete spectrum of symplectic groups up to global Arthur packets, based on the theory of endoscopy. It is an interesting and basic question to ask: which global Arthur packets contain no…

In his monograph (2013) Arthur characterizes the L-packets of quasisplit symplectic groups and orthogonal groups. By extending his work, we characterize the L-packets for the corresponding similitude groups with desired properties. In…

Arthur has conjectured that the unitarity of a number of representations can be shown by finding appropriate automorphic realizations. This has been verified for classical groups by Moeglin and for the exceptional Chevalley group G_2 by…

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

Let $G(k)$ be the split form of the simple exceptional p-adic group of type $F_4$, and let $\mathcal O = F_4(a_3)$ be the minimal distinguished nilpotent orbit. Our main result concerns the class of unipotent representations with cuspidal…

In this paper, we determine all the Arthur packets containing an irreducible unitary lowest weight representation $\pi$ of real unitary group $G = \mathrm{U}(p, q)$, including non-scalar cases. Our methods are the Barbasch-Vogan…

In [HJLLZ24], we proposed a new conjecture on the structure of the unitary dual of connected reductive groups over non-Archimedean local fields of characteristic zero based on their Arthur representations and verified it for all the known…

We compute special unipotent Arthur packets for real reductive groups in many cases. We list the cases that lead to incomplete answers, and in those cases, provide a suitable set of representations that could lead to a complete description…

In this paper, following Arthur's ideas, we rework the process of constructing the anti-tempered local Arthur packets for quasi-split classical groups and their pure inner forms. In particular, we present explicit examples illustrating…

In this paper we establish the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over…

Let $\mathbf{G}$ be an unramified quasi-split unitary group over a p-adic field of odd residual characteristic. The goal of this paper is to describe the supercuspidal representations within certain L-packets of $\mathbf{G}$, which are…

In their study of Arthur's conjectures for real groups, Adams, Barbasch, and Vogan introduced the notion of micro-packets. Micro-packets are finite sets of irreducible representations defined using microlocal geometric methods and…

Arthur's conjectures predict the existence of some very interesting unitary representations occurring in spaces of automorphic forms. We prove the unitarity of the "Langlands element" (i.e., the one specified by Arthur) of all unipotent…

In this paper, we propose a new conjecture describing the structure of the unitary dual in terms of Arthur representations for connected reductive algebraic groups defined over any non-Archimedean local field of characteristic zero. This…

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…

In this article we propose a geometric description of Arthur packets for $p$-adic groups using vanishing cycles of perverse sheaves. Our approach is inspired by the 1992 book by Adams, Barbasch and Vogan on the Langlands classification of…

On montre comment les conjectures d'Arthur permettent de calculer les points de r\'eductibilit\'e pour les induites de cuspidales des groupes classiques. Les conjectures d'Arthur utilis\'ees portent sur l'existence d'un rel\`evement faible…

In the spirit of Arthur's trace formula, we establish a general trace formula for symmetric spaces associated with the variety of involutions of a finite $D$-module where $D$ is a division algebra central over a number field $F$. Such a…

In this paper, applying the intersection theory of local Arthur packets, for symplectic and split odd special orthogonal groups G_n, we give the first complete proof of the enhanced Shahidi conjecture on generic representations in local…