Related papers: Two-point Functions in Affine Current Algebra and …
The main principle of affine quantum gravity is the strict positivity of the matrix \{\hat g_{ab}(x)\} composed of the spatial components of the local metric operator. Canonical commutation relations are incompatible with this principle,…
We obtain a characterization of the real Lie algebras admitting abelian complex structures in terms of certain affine Lie algebras $\frak a \frak f \frak f (A)$, where $A$ is a commutative algebra. These affine Lie algebras are natural…
We introduce the notion of extended affine Lie superalgebras and investigate the properties of their root systems. Extended affine Lie algebras, invariant affine reflection algebras, finite dimensional basic classical simple Lie…
This is the first in a series of papers which describe the action of an affine Lie algebra with central charge $n$ on the moduli space of $U(n)$-instantons on a four manifold $X$. This generalises work of Nakajima, who considered the case…
We compute the most general embedding space two-point function in arbitrary Lorentz representations in the context of the recently introduced formalism in arXiv:1905.00036 and arXiv:1905.00434. This work provides a first explicit…
This article presents simple and easy proofs of the Implicit Function Theorem and the Inverse Function Theorem, in this order, both of them on a finite-dimensional Euclidean space, that employ only the Intermediate Value Theorem and the…
This paper introduces calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The primary technique is to provide indexing sets for controlling the…
The set of points of a one-dimensional cut-and-project quasicrystal or model set, while not additive, is shown to be multiplicative for appropriate choices of acceptance windows. This leads to the definition of an associative additive…
A model of two--dimensional gravity with an action depending only on a linear connection is considered. This model is a topological one, in the sense that the classical action does not contain a metric or zweibein at all. A metric and an…
It is shown that any Lie affgebra, that is an algebraic system consisting of an affine space together with a bi-affine bracket satisfying affine versions of the antisymmetry and Jacobi identity, is isomorphic to a Lie algebra together with…
We construct and study in detail various dual pairs acting on some Fock representations between a finite dimensional Lie group and a completed infinite rank affine algebra associated to an infinite affine Cartan matrix. We give explicit…
We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley--Sohoni Geometric Complexity Theory program. A matrix Lie…
We show that the following two algebras are isomorphic. The first is the algebra $A_P$ of functions on the scheme of monic linear second-order differential operators on $\C$ with prescribed regular singular points at $z_1,..., z_n, \infty$,…
Lie algebras are extended to the affine case using the heap operation, giving them a definition that is not dependent on the unique element 0, such that they still adhere to antisymmetry and Jacobi properties. It is then looked at how…
For any root system corresponding to a semisimple simply-laced Lie algebra a logarithmic CFT is constructed. Characters of irreducible representations were calculated in terms of theta functions.
We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…
In two-dimensional conformal field theory (CFT) the building blocks are given by chiral CFTs, i.e.~CFTs on the unit circle (compactified light-ray). They are generated by quantum fields depending on one light-ray coordinate only. There are…
It is shown that every two-variable adjunction in categories enriched in a commutative quantale serves as a base for constructing Isbell adjunctions between functor categories, and Kan adjunctions are precisely Isbell adjunctions…
Four types of discrete transforms of Weyl orbit functions on the finite point sets are developed. The point sets are formed by intersections of the dual-root lattices with the fundamental domains of the affine Weyl groups. The finite sets…
We prove that two fixed univariate functions, namely, an arbitrary continuous non-affine function and a concrete affine function, are sufficient to approximate continuous functions of one variable under the operations of addition and…