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We establish the generic local Langlands correspondence by showing the equality of the Langlands-Shahidi $L$-functions and Artin $L$-functions in the case of even unitary similitude groups. As an application, we prove both weak and strong…

Number Theory · Mathematics 2025-06-03 Yeansu Kim , Muthu Krishnamurthy , Freydoon Shahidi

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…

Representation Theory · Mathematics 2022-01-05 Hiraku Atobe

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…

Number Theory · Mathematics 2022-01-03 Dihua Jiang , Baiying Liu

For metaplectic groups over a local field of characteristic zero, we define the Arthur packet attached to any Arthur parameter $\psi$ as a multi-set of unitary genuine irreducible representations, characterized by endoscopic character…

Representation Theory · Mathematics 2024-11-14 Wen-Wei Li

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…

Number Theory · Mathematics 2024-08-22 Baiying Liu , Chi-Heng Lo , Freydoon Shahidi

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…

Representation Theory · Mathematics 2026-02-11 Alexander Hazeltine , Dihua Jiang , Baiying Liu , Chi-Heng Lo , Qing Zhang

The purpose of this paper is to show that under a part of generalized Arthur's A-packet conjecture, locally generic cuspidal automorphic representations of a quasisplit group over a number field are of Ramanujan type, i.e., are tempered at…

Number Theory · Mathematics 2015-01-14 Freydoon Shahidi

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…

Representation Theory · Mathematics 2022-09-16 Nicolas Arancibia Robert , Paul Mezo

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…

Representation Theory · Mathematics 2017-03-01 Bin Xu

A Langlands parameter, in the Langlands dual group, can be decomposed into a product of a tempered parameter and a positive quasi-character. Fixing a tempered parameter, Arthur conjectured that positive quasi-characters corresponding to…

Representation Theory · Mathematics 2013-03-20 Hongyu He

Nous \'etendons aux groupes orthogonaux et unitaires non quasi-d\'eploy\'es sur un corps local des r\'esultats de J. Arthur et de la premi\`ere auteure \'etablis dans le cas quasi-d\'eploy\'e. En particulier, nous obtenons une…

Representation Theory · Mathematics 2018-03-22 Colette Moeglin , David Renard

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…

Representation Theory · Mathematics 2025-05-26 Alexander Hazeltine , Dihua Jiang , Baiying Liu , Chi-Heng Lo , Qing Zhang

In this paper we prove the forward direction of the conjecture of Gross-Prasad that an L-packet $\Pi_\phi(G)$ contains a generic representation if and only if $L(s, \phi, \Ad)$ is regular at $s=1$, by assuming the local Langlands…

Representation Theory · Mathematics 2025-06-03 Kristaps Balodis , Clifton Cunningham , Andrew Fiori , Qing Zhang

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…

Representation Theory · Mathematics 2023-08-10 Raúl Alonso , Qiao He , Mishty Ray , Martí Roset

In this paper, we reformulate Moeglin's explicit construction of local A-packets of split odd special orthogonal groups and symplectic groups. By this reformulation together with results of the previous paper with Minguez, we can compute…

Representation Theory · Mathematics 2022-04-26 Hiraku Atobe

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…

Number Theory · Mathematics 2012-12-10 Paul-James White

Nous d\'ecrivons explicitement les paquets d'Arthur des groupes classiques complexes, ainsi que leur param\'etrisation interne par les caract\`eres du groupe des composantes connexes du centralisateur de leur param\`etre. Nous montrons…

Representation Theory · Mathematics 2017-05-12 Colette Moeglin , David Renard

We show that ABV-packets for $p$-adic groups do not depend on the choice of a Whittaker datum, but the function from the ABV-packet to representations of the appropriate microlocal equivariant fundamental group does, and we find this…

Representation Theory · Mathematics 2024-12-11 Clifton Cunningham , Sarah Dijols , Andrew Fiori , Qing Zhang

Zelevinsky's classification theory of discrete series of $p$-adic general linear groups has been well known. M{\oe}glin and Tadic gave the same kind of theory for $p$-adic classical groups, which is more complicated due to the occurrence of…

Representation Theory · Mathematics 2017-02-16 Bin Xu

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…

Representation Theory · Mathematics 2025-08-27 Shuji Horinaga