Related papers: Unramified two-dimensional Langlands correspondenc…

This paper surveys what is known about (conjectural) $p$-adic and $p$-modular semisimple Langlands correspondences in the non-supercuspidal setting for the unramified quasi-split unitary group…

Over a global field any finite number of central simple algebras of exponent dividing $m$ is split by a common cyclic field extension of degree $m$. We show that the same property holds for function fields of two-dimensional excellent…

Using the theta correspondence, we extend the classification of irreducible representations of quasi-split unitary groups (the so-called local Langlands correspondence, which was established in an early paper of Mok) to non quasi-split…

Let G be any reductive p-adic group. We discuss several conjectures, some of them new, that involve the representation theory and the geometry of G. At the heart of these conjectures are statements about the geometric structure of Bernstein…

We work out the unfolded formulation of the fields in the non-linear realisation of $E_{11}$. Using the connections in this formalism, we propose, at the linearised level, an infinite number of first-order duality relations between the dual…

We introduce the cotangent universal hierarchy that extends the so-called universal hierarchy (as for the latter, see e.g. arXiv:nlin/0202008, arXiv:nlin/0312043 and arXiv:nlin/0310036). Then we construct a (2+1)-dimensional double central…

Slicing a module into semisimple ones is useful to study modules. Loewy structures provide a means of doing so. To establish the Loewy structures of projective modules over a finite dimensional symmetric algebra over a field $F$, the…

This paper establishes a relationship between finite extensions and norm groups of formally real quasilocal fields, which yields a generally nonabelian local class field theory, including analogues to the fundamental correspondence, the…

We investigate the most general non(anti)commutative geometry in N=1 four-dimensional superspace, invariant under the classical (i.e., undeformed) supertranslation group. We find that a nontrivial non(anti)commutative superspace geometry…

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…

It is shown that the geometry of parallelizable manifolds can be extended to non-parallelizable ones by extending the connection that a global frame field would define on a parallelizable manifold to a connection that a singular frame field…

In 1967, Langlands conjectured a natural correspondence between automorphic representations and Galois representations, over number fields as well as over function fields. In 1983, Drinfeld discovered a geometric analog of the Langlands…

It is outlined how deformations of field theoretical rigid symmetries can be constructed and classified by cohomological means in the extended antifield formalism. Special attention is devoted to deformations referring only to a subset of…

Let F be a non-archimedean local field and let O be its ring of integers. We give a complete description of the irreducible constituents of the restriction of the unramified principal series representations of GL(3,F) to GL(3,O).

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,…

Proper classes of extensions of real field was defined and topological properties of these extensions were studied. These extensions can be connected, in this case such set is not closed under binary operations (addition and…

The reciprocity law for abelian differentials of first and second kind is generalized to higher-dimensional varieties. It is shown that $H^1(V)$ of a polarized variety $V$ is encoded in the Laurent data along a curve germ in $V$, with the…

The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras as well as central extension procedure are presented. The…

We analyze the universality of the bosonization rules in non-relativistic fermionic systems in $(2+1)d$. We show that, in the case of linear fermionic dispersion relations, a general fermionic theory can be mapped into a gauge theory in…

We complete the first stage of constructing a theory of fields not investigated before; these fields transform according to Lorentz group representations decomposable into an infinite direct sum of finite-dimensional irreducible…