Related papers: Finite Langlands correspondence

We define Langlands parameters for connected reductive groups over finite fields and formulate the Langlands correspondence for finite fields using these parameters.

We discuss progress towards the classification of irreducible admissible representations of reductive groups over non-archimedean local fields and the local Langlands correspondence. We also state some (partly conjectural) compatibility…

The geometric Langlands correspondence for function fields over finite fields has been proved by Frenkel, Gaitsgory, Vilonen. The aim of this article is to write translation for curves over the complex field and prove the correspondence in…

Let $\ell$ be a prime number different from the residue characteristic of a non-archimedean local field $F$. We give formulations of $\ell$-adic local Langlands correspondences for connected reductive algebraic groups over $F$, which we…

This work is intended as an introduction to the statement and the construction of the local Langlands correspondence for GL(n) over p-adic fields. The emphasis lies on the statement and the explanation of the correspondence.

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…

These notes collect results about algebraic correspondences and adapt them to the setting of correspondences on projective lines. The focus lies on finite orbits of algebraic correspondences. The main result is a field theoretic…

We show that, over a nonarchimedean local field, the rigid refined local Langlands correspondence and associated endoscopic character identities for connected reductive $G$ follow if one only has them for all such $G$ with connected center.…

In this paper we describe the unramified Langlands correspondence for two-dimensional local fields, we construct a categorical analogue of the unramified principal series representations and study its properties. The main tool for this…

In one of our previous articles, we outlined the formulation of a version of the categorical arithmetic local Langlands conjecture. The aims of this article are threefold. First, we provide a detailed account of one component of this…

These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…

We formulate the local Langlands conjecture for connected reductive groups over local fields, including the internal parametrization of L-packets using endoscopy.

We establish the Geometric Langlands correspondence for rank one groups over the projective line with three points of tame ramification.

In this paper, we continue the work of the first author and give a new construction of the tame local Langlands correspondence for PGSp(4,F), where F is a p-adic field, that is analogous to the construction of the local Langlands…

Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group $SL_n (F)$. It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for…

We survey several recent examples of derived structures emerging in connection with the Langlands correspondence. Cases studies include derived Galois deformation rings, derived Hecke algebras, derived Hitchin stacks, and derived special…

Consider the irreducible representations of a real reductive group $G(\mathbb{R})$, and their parametrization by the local Langlands correspondence. We ask: does the parametrization give easily accessible information on the restriction of…

Using theta correspondence, we obtain a classification of irreducible representations of an arbitrary even orthogonal group (i.e. the local Langlands correspondence) by deducing it from the local Langlands correspondence for symplectic…

We classify the finite connected-homogeneous digraphs, as well as the infinite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.

Finite Lorentz groups acting on 4-dimensional vector spaces coordinatized by finite fields with a prime number of elements are represented as homomorphic images of countable, rational subgroups of the Lorentz group acting on real…