相关论文: Parameters and duality for the metaplectic geometr…
Symplectic vector spaces are the phase spaces of linear mechanical systems. The symplectic form describes, for example, the relation between position and momentum as well as current and voltage. The category of linear Lagrangian relations…
We prove a formula for the global gravitational anomaly of the self-dual field theory in the presence of background gauge fields, assuming the results of arXiv:1110.4639. Along the way, we also clarify various points about the self-dual…
This paper explores relations between two separate worlds. They are the algebraic geometry of Alexander Grothendieck and the automorphic representation theory of Robert Langlands. The relation between them would be a very broad example of…
Over a $p$-adic local field $F$ of characteristic zero, we develop a new type of harmonic analysis on an extended symplectic group $G={\mathbb G}_m\times{\mathrm Sp}_{2n}$. It is associated to the Langlands $\gamma$-functions attached to…
Recently we propose a class of infinite-dimensional integral representations of classical gl(n+1)-Whittaker functions and local Archimedean local L-factors using two-dimensional topological field theory framework. The local Archimedean…
In this note, we study the local relative geometric Langlands conjecture of Ben-Zvi--Sakellaridis--Venkatesh for the spherical subgroup $\mathrm{PGL}_2^\mathrm{diag}$ of the triple product $\mathrm{PGL}_2^{\times 3}$ (and also for the…
We define a new geometric object--the stack of local systems with restricted variation. We formulate a version of the categorical geometric Langlands conjecture that makes sense for any constructible sheaf theory (such as l-adic sheaves).…
$2$-form abelian and non-abelian gauge fields on $d$-dimensional hypercubic lattices have been discussed in the past by various authors and most recently by Lipstein and Reid-Edwards. In this note we recall that the Hamiltonian of a…
Let $F$ be a locally compact non-Archimedean field of characteristic $0$, and let $G$ be either the split special orthogonal group $\mathrm{SO}_{2n+1}(F)$ or the symplectic group $\mathrm{Sp}_{2n}(F)$. The goal of this paper is to give an…
We discuss the recent proposal of implementing Doubly Special Relativity in configuration space by means of Finsler geometry. Although this formalism leads to a consistent description of the dynamics of a particle, it does not seem to give…
By the geometric Satake correspondence, the number of components of certain fibres of the affine Grassmannian convolution morphism equals the tensor product multiplicity for representations of the Langlands dual group. On the other hand, in…
We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended…
By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their…
We lay out an infinity categorical interpretation of reconstruction theorems which are germane to the symmetric monoidal perspective of noncommutative algebraic geometry, present sufficient conditions which allow for the factorization of…
We relate duality mappings to the "Babbage equation" F(F(z)) = z, with F a map linking weak- to strong-coupling theories. Under fairly general conditions F may only be a specific conformal transformation of the fractional linear type. This…
A gauge $\gamma$ in a vector space $X$ is a distance function given by the Minkowski functional associated to a convex body $K$ containing the origin in its interior. Thus, the outcoming concept of gauge spaces $(X, \gamma)$ extends that of…
Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles naturally. The application of Grassmannian duality cuts down the number of states substantially and is vital for constructing…
The gauge theory approach to the geometric Langlands program is extended to the case of wild ramification. The new ingredients that are required, relative to the tamely ramified case, are differential operators with irregular singularities,…
The paper explores categorical interconnections between lattice-valued Relational systems and algebras of Fitting's lattice-valued modal logic. We define lattice-valued boolean systems, and then we study co-adjointness, adjointness of…
We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient…