Related papers: Some Unipotent Arthur Packets for Reductive $p$-ad…

Let $(\pi,X)$ be a depth-$0$ admissible smooth complex representation of a $p$-adic reductive group that splits over an unramified extension. In this paper we develop the theory necessary to study the wavefront set of $X$ over a maximal…

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…

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…

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.…

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…

We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups. We prove Arthur's conjecture, the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group, for quasi-split special unitary groups…

We generalize the work of DeBacker and Reeder to the case of unitary groups split by a tame extension. The approach is broadly similar and the restrictions on the parameter the same, but many of the details of the arguments differ. Let $G$…

For an irreducible smooth representation of a connected reductive $p$-adic group, two important associated invariants are the wavefront set and the (partly conjectural) Langlands parameter. While a wavefront set consists of $p$-adic…

Let G be a group SO(2n+1) defined over a p-adic field. We compute the wave front set of the anti-tempered irreducible representations of G(F) which are of unipotent reduction. It is the orthogonal orbit dual to the symplectic orbit…

Let $G \subseteq \tilde{G}$ be two quasisplit connected reductive groups over a local field of characteristic zero and $G_{der} = \tilde{G}_{der}$. Although the existence of L-packets is still conjectural in general, it is believed that the…

In this paper we gives the Langlands parameters of Langlands' packets of discrete series using the twisted endoscopy as explained by Arthur; this holds for orthogonal, symplectic, unitary and G-Spin groups and gives the most simple proof…

For a real group $G$, it is known from the work of Kostant and Vogan that the L-packet associated with an L-parameter $\varphi$ of $G$ contains a \emph{generic} representation if and only if the ${}^{\vee}G$-orbit in the variety 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…

The aim of this work, is to describe fairly explicitly a general Arthur's packet for a classical group. The problem to be solved, here, is the decompostion of induced representations. Following previous work on general linear group, such a…

By computing reducibility points of parabolically induced representations, we construct, to within at most two unramified quadratic characters, the Langlands parameter of an arbitrary depth zero irreducible cuspidal representation $\pi$ of…

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 give a survey on M{\oe}glin's construction of representations in the Arthur packets for $p$-adic quasisplit symplectic and orthogonal groups. The emphasis is on comparing M{\oe}glin's parametrization of elements in the Arthur packets…

There exists a significant conjecture in the local Langlands correspondence that A-packets are ABV-packets. For the case $G=GL_n$, the conjecture reduces to ABV-packets for orbits of Arthur type in $GL_n$ being singletons, which is a…

Let $\pi, \pi'$ be tempered representations of an affine Hecke algebra with positive parameters. We study their Euler--Poincar\'e pairing $EP (\pi,\pi')$, the alternating sum of the dimensions of the Ext-groups. We show that $EP (\pi,\pi')$…

We develop a general procedure to study the combinatorial structure of Arthur packets for $p$-adic quasisplit $Sp(N)$ and $O(N)$ following the works of M{\oe}glin. This allows us to answer many delicate questions concerning the Arthur…