Related papers: A `relative' local Langlands correspondence

Hiraga, Ichino and Ikeda have conjectured an explicit expression for the Plancherel density of the group of points of a reductive group defined over a local field $F$, in terms of local Langlands parameters. In these lectures we shall…

In all forms of the local Langlands program the abelian category of smooth representations of p-adic groups G in vector spaces over a field k plays a central role. Of particular interest are its finiteness properties. If the field k has…

Let G be a classical p-adic group and $(\psi ,\epsilon)$ the Langlands parameter of an irreducible supercuspidal representation of a Levi subgroup of G. Using data from $(\psi ,\epsilon)$, we determine explicitly the intertwining algebra of…

We construct the local Langlands correspondence of essentially unipotent supercuspidal representations under the framework of rigid inner forms and prove a certaion functoriality and compatibilities. This result is stronger than the…

We construct a Langlands parameterization of supercuspidal representations of $G_2$ over a $p$-adic field. More precisely, for any finite extension $K / \QQ_p$ we will construct a bijection \[ \CL_g : \CA^0_g(G_2,K) \rightarrow \CG^0(G_2,K)…

We introduce and motivate -- based on ongoing joint work with Germ\'an Stefanich -- the notion of potent categorical representations of a complex reductive group $G$, specifically a conjectural Langlands correspondence identifying potent…

We prove the local Langlands correspondence for GSp_4(F), where F is a non-archimedean local field of positive characteristic with residue characteristic > 2.

We state a conjecture, local Langlands in families, connecting the centre of the category of smooth representations on $\mathbb{Z}[\sqrt{q}^{-1}]$-modules of a quasi-split $p$-adic group $\mathrm{G}$ (where $q$ is the cardinality of the…

We construct the Langlands correspondence for connected reductive groups over finite fields, which we call the finite Langlands correspondence. We discuss also its relation with the categorical local Langlands correspondence.

Let $F$ be a non-Archimedian local field of characteristic zero and $E/F$ a quadratic extension. The aim of the present article is to study the multiplicity of an irreducible admissible representation of ${\rm GL}_2(F)$ occurring in an…

This article is on the parametrization of the local Langlands correspondence over local fields for non-quasi-split groups according to the philosophy of Vogan. We show that a parametrization indexed by the basic part of the Kottwitz set…

Let E be a nonarchimedean local field with residue characteristic l, and suppose we have an n-dimensional representation of the absolute Galois group G_E of E over a reduced complete Noetherian local ring A with finite residue field k of…

Let G be a general linear group over a p-adic field and let D^* be an anisotropic inner form of G. The Jacquet-Langlands correspondence between irreducible complex representations of D^* and discrete series of G does not behave well with…

Let $F$ be a totally real number field, $\wp$ a place of $F$ above $p$. Let $\rho$ be a $2$-dimensional $p$-adic representation of $\mathrm{Gal}(\bar{F}/F)$ which appears in the \'etale cohomology of quaternion Shimura curves (thus $\rho$…

Motivated by the study of trilinear forms for complex representations, we investigate the space of $G$-invariant linear forms on tensor products of irreducible admissible representations of $G = \mathrm{GL}_2(\mathbb{Q}_p)$ over…

Let $F$ be a $p$-adic field and $E/F$ be a quadratic extension. In this paper, we prove the local converse theorem for generic representations of $\textrm{U}_{E/F}(2,2)$ if $E/F$ is unramified or the residue characteristic of $F$ is odd.…

Let G be a quasi-split reductive group over a non-archimedean local field. We establish a local Langlands correspondence for all irreducible smooth complex G-representations in the principal series. The parametrization map is injective, and…

We prove the local Langlands conjecture for the exceptional group $G_2(F)$ where $F$ is a non-archimedean local field of characteristic zero.

The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After…

Let $p$ be a prime number, $F $ a non-archimedean local field with residue characteristic $p$, and $R$ an algebraically closed field of characteristic different from $ p$. We thoroughly investigate the irreducible smooth $R$-representations…