Related papers: Arthur packets for $G_2$ and perverse sheaves on c…

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…

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…

We develop a general strategy for constructing the explicit Local Langlands Correspondences for $p$-adic reductive groups via reduction to LLC for supercuspidal representations of proper Levi subgroups, using Hecke algebra techniques. As an…

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…

Let $G$ be a complex reductive algebraic group. In arXiv:2108.03453, we have defined a finite set of irreducible admissible representations of $G$ called `unipotent representations', generalizing the special unipotent representations of…

In spirit of Gan-Ichino's work on the Arthur's multiplicity formula for metaplectic groups, we have established the Arthur's multiplicity formula for even orthogonal or unitary groups with Witt index less than or equal to one. In that…

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…

This paper is an introduction to the use of perverse sheaves with positive characteristic coefficients in modular representation theory. In the first part, we survey results relating singularities in finite and affine Schubert varieties and…

Let G be a connected unipotent group over a finite field F_q with q elements. In this article we propose a definition of L-packets of complex irreducible representations of the finite group G(F_q) and give an explicit description of…

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…

For a connected reductive group $G$ over ${\mathbb R}$, we study cohomological $A$-parameters, which are Arthur parameters with the infinitesimal character of a finite-dimensional representation of $G({\mathbb C})$. We prove a structure…

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…

We classify the unitary representations with integral infinitesimal character in Lusztig's category of unipotent representations in the case when the geometric parameter space comes from the action of a Levi subgroup on the abelian…

In 1993 David Vogan proposed a basis for the vector space of stable distributions on $p$-adic groups using the microlocal geometry of moduli spaces of Langlands parameters. In the case of general linear groups, distribution characters of…

We generalise to the equivariant case a result of J. Denef and F. Loeser about trigonometric sums on tori; on the other hand, we study the Thom-Boardman stratification associated to the multiplication of global sections of line bundles on a…

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…

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…

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 [J14], a conjecture was proposed on a relation between the global Arthur parameters and the structure of Fourier coefficients of the automorphic representations in the corresponding global Arthur packets. In this paper, we discuss the…

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…