Related papers: Relative Langlands Duality

In [Rie08], the second author defined a Landau-Ginzburg model for homogeneous spaces G/P, as a regular function on an affine subvariety of the Langlands dual group. In this paper, we reformulate this LG-model (X^,W_t) in the case of the…

We introduce a category of dual pairs of finite locally free algebras over a ring. This gives an efficient way to represent finite locally free commutative group schemes. We give a number of algorithms to compute with dual pairs of…

Two field 2-forms on the space-time manifold, in a relationship of duality, are presented and included in the extended phase-space structure used to describe relativistic particles having both electric and magnetic charges. By exterior…

We initiate the study of the duality theory of locally recoverable codes, with a focus on the applications. We characterize the locality of a code in terms of the dual code, and introduce a class of invariants that refine the classical…

The aim of these notes is to give an overview of several aspects of what has come to be called the relative Langlands program, a theme that takes its origin in the study of automorphic periods and their relations to particular cases of…

We consider duality transformations in N=2 Yang--Mills theory coupled to N=2 supergravity, in a manifestly symplectic and coordinate covariant setting. We give the essential of the geometrical framework which allows one to discuss stringy…

We argue that a special step in the chain of dualities used in [Tan 2008] implicitly suggests to view Langlands duality as being fundamentally rooted in an eight-dimensional theory on the F-theory 7- brane. We give further arguments why…

We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian…

Let $G_\mathbb R$ be a connected real reductive group and let $X$ be the corresponding complex symmetric variety under the Cartan bijection. We construct a canonical equivalence between the relative Satake category of $G(\mathcal…

Let G be a connected reductive complex algebraic group. This paper is devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical G-variety X. The space Z may be thought of as an algebraic model for the loop space…

We incorporate metric data into the framework of Tannaka-Krein duality. Thus, for any group with left invariant metric, we produce a dual metric on its category of unitary representations. We characterize the conditions under which a…

We describe the doubled space of Double Field Theory as a group manifold $G$ with an arbitrary generalized metric. Local information from the latter is not relevant to our discussion and so $G$ only captures the topology of the doubled…

Weak-strong coupling duality relations are shown to be present in the quantum-mechanical many-body system with the interacting potential proportional to the pair-wise inverse-squared distance in addition to the harmonic potential. Using…

We introduce and study a notion of duality for two classes of optimization problems commonly occurring in probability theory. That is, on an abstract measurable space $(\Omega,\mathcal{F})$, we consider pairs $(E,\mathcal{G})$ where $E$ is…

Langlands' functoriality principle predicts deep relations between the local and automorphic spectra of different reductive groups. This has been generalized by the relative Langlands program to include spherical varieties, among which…

In a previous paper, the first and third authors gave an explicit realization of the geometric Langlands correspondence for hypergeometric sheaves, considered as $\textrm{GL}_n$-local systems. Certain hypergeometric local systems admit a…

We formulate the normalized period conjecture proposed by Ben-Zvi, Sakellaridis and Venkatesh in the framework of the categorical local Langlands correspondence and study its relation to distinction problems. Motivated by the work of Feng…

For any causal nonlinear electrodynamics theory that is "self-dual" (electromagnetic $U(1)$-duality invariant), the Legendre-dual pair of Lagrangian and Hamiltonian densities $\{\mathcal{L},\mathcal{H}\}$ are constructed from functions…

Imposing T-duality in the renormalisation process of entanglement entropy leads to new relations between entanglement entropy counter-terms. T-duality is made explicit by means of the generalised metric of double field theory in the context…

Doubling a Yang-Mills field we apply the pattern which has been found to construct a "duality-symmetric" gravity with matter to the "duality-symmetric" Yang - Mills theory in five space-time dimensions. Constructing the action we conclude…