Related papers: n-Dimensional global correspondences of Langlands

A rather complete phenomenology of the singularities is developed according to a new algebraic point of view in the frame of Langlands global correspondences. That is to say,a process of: -singularizations and versal deformations of these,…

All kinds of global correspondences of Langlands are evaluated from the functional representation spaces of the algebraic bilinear semigroups GL2(.x.) with entries in products,right by left,of sets of archimedean increasing completions.…

Selfdual representations of any group fall into two classes when they are irreducible: those which carry a symmetric bilinear form, and the others which carry an alternating bilinear form. The Langlands correspondence, which matches the…

An algebraic extended bilinear Hilbert semispace is proposed as being the natural representation space for the algebras of von Neumann.This bilinear Hilbert semispace has a well defined structure given by the representation space of an…

A brief survey is given of the classical Langlands correspondence between n-dimensional representations of Galois groups of local and global fields of dimension 1 and irreducible representations of the groups GL(n). A generalization of the…

The paper revisits concretely the algebraic K-theory in the light of the global program of Langlands by taking into account the new algebraic interpretation of homotopy viewed as deformation(s) of Galois representations given by…

Let $F$ be a non-Archimedean local field of residual characteristic $p$, and $\ell$ a prime number, $\ell \neq p$. We consider the Langlands correspondence, between irreducible, $n$-dimensional, smooth representations of the Weil group of…

Let F be a non-Archimedean local field and let E be an unramified extension of F of degree n>1. To each sufficiently generic multiplicative character of E (the details are explained in the body of the paper) one can associate an irreducible…

The Weil representation is a particularly significant linear representation of the metaplectic group, used in the study of theta correspondence. In this paper, I introduce a derived category version of the Weil representation in the local…

We give presentations, in terms of the generators and relations, for the reflection equation algebras of type $GL_n$ and $SL_n$, i.e., the covariantized algebras of the dual Hopf algebras of the small quantum groups of $\mathfrak{gl}_n$ and…

Let H be any reductive p-adic group. We introduce a notion of cuspidality for enhanced Langlands parameters for H, which conjecturally puts supercuspidal H-representations in bijection with such L-parameters. We also define a cuspidal…

This paper deals with the geometric local theta correspondence at the Iwahori level for dual reductive pairs of type II over a non Archimedean field $F$ of characteristic $p\neq 2$ in the framework of the geometric Langlands program. First…

The object of this article is to study some aspects of the quantum geometric Langlands program in the language of vertex algebras. We investigate the representation theory of the vertex algebra of chiral differential operators on a…

Let G be a connected reductive group over a non-archimedean local field. We say that an irreducible depth-zero (complex) G-representation is non-singular if its cuspidal support is non-singular. We establish a Local Langlands Correspondence…

This third paper,devoted to global correspondences of Langlands,bears more particularly on geometric-shifted bilinear correspondences on mixed (bi)motives generated under the action of the products,right by left,of differential elliptic…

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 introduce the notions of symmetric and symmetrizable representations of $\text{SL}_2(\mathbb{Z})$. The linear representations of $\text{SL}_2(\mathbb{Z})$ arising from modular tensor categories are symmetric and have congruence kernel.…

Let G be a connected reductive group over a non-archimedean local field K, and assume that G splits over an unramified extension of K. We establish a local Langlands correspondence for irreducible unipotent representations of G. It comes as…

In this paper we describe the set of conjugacy classes in the group SL(n,Z). We expand geometric Gauss Reduction Theory that solves the problem for SL(2,Z) to the multidimensional case. Further we find complete invariant of classes in terms…

We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…