Related papers: Extended geometries
In this paper, generalized metrics mean metrics taking values in general linearly ordered Abelian groups. Using the Hahn fields, we first prove that for every generalized metric space, if the set of the Archimedean equivalence classes of…
The method of graded contractions, based on the preservation of the automorphisms of finite order, is applied to the affine Kac-Moody algebras and their representations, to yield a new class of infinite dimensional Lie algebras and…
The group of vertical diffeomorphisms of a principal bundle forms the generalised action Lie groupoid associated to the bundle. The former is generated by the group of maps with value in the structure group, which is also the group of…
We review the higher gauge symmetries in double and exceptional field theory from the viewpoint of an embedding tensor construction. This is based on a (typically infinite-dimensional) Lie algebra $\frak{g}$ and a choice of representation…
We give variants of lifting construction, which define new classes of modular forms on the Siegel upper half-space of complex dimension 3 with respect to the full paramodular groups (defining moduli of Abelian surfaces with arbitrary…
In any dimension, the positive level generators of the very-extended Kac-Moody algebra $E_{11}$ with completely antisymmetric spacetime indices are associated to the form fields of the corresponding maximal supergravity. We consider the…
A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an abelian ideal. When the superalgebra is of affine Kac-Moody type, a generalisation of…
In a recent paper, it was shown that in diffeomorphism-invariant theories, Noether charges associated with a given codimension-2 surface become integrable if one introduces an extended phase space. In this paper we extend the notion of…
We introduce an affinization of the quantum Kac-Moody algebra associated to a symmetric generalized Cartan matrix. Based on the affinization, we construct a representation of the quantum Kac-Moody algebra by vertex operators from bosonic…
We present a geometric construction of highest weight crystals for quantum generalized Kac-Moody algebras. It is given in terms of the irreducible components of certain Lagrangian subvarieties of Nakajima's quiver varieties associated to…
We introduce exceptional field theory for the group E_{7(7)}, based on a (4+56)-dimensional spacetime subject to a covariant section condition. The `internal' generalized diffeomorphisms of the coordinates in the fundamental representation…
Let $Y$ be a CW-complex with a single 0-cell, $K$ its Kan group, a model for the loop space of $Y$, and let $G$ be a compact, connected Lie group. We give an explicit finite dimensional construction of generators of the equivariant…
The present paper is revised copy of hep-th/9303087 in which higher spin extensions of the nonabelian gauge symmetries for the classical WZNW model are considered. Both linear and nonlinear realizations of the extended affine Kac-Moody…
In the first paper of this sequence, we provided an explicit hypergeometric modularity method by combining different techniques from the classical, $p$-adic, and finite field settings. In this article, we explore an application of this…
We present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups E_n(n). We then consider "tensor gauge fields" coupled to…
We construct finite- and infinite-dimensional non-relativistic extensions of the Newton-Hooke and Carroll (A)dS algebras using the algebra expansion method, starting from the (anti-)de Sitter relativistic algebra in D dimensions. These…
We construct Wakimoto modules for twisted affine Lie algebras, and interpret the construction in terms of vertex algebras and their twisted modules. Using the Wakimoto realization, we prove the Kac-Kazhdan conjecture on the characters of…
We define Weyl functors, global modules for equivariant map Lie superalgebras $(\g \otimes A)^{\Gamma}$, where $\g$ is basic classical $\mathbb{C}$- Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}$-algebra. Under…
Invariant affine reflection algebras are the last and the most general known extension of affine Kac-Moody Lie algebras, introduced in recent years. We develop a method known as "affinization" to the class of invariant affine reflection…
In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…