Journal ArticleDOI
Introduction to lie algebras and representation theory
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This article is published in Bulletin of The London Mathematical Society.The article was published on 1974-07-01. It has received 844 citations till now. The article focuses on the topics: Adjoint representation of a Lie algebra & Representation of a Lie group.read more
Citations
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Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality
TL;DR: The Wilson-t Hooft operator as mentioned in this paper is a topologically nontrivial operator that is localized on a straight line, creates electric and magnetic flux, and in the UV limit breaks the conformal invariance in the minimal possible way.
Journal ArticleDOI
Symmetric invariant bilinear forms on vertex operator algebras
TL;DR: In this paper, a criterion for determining the existence of nonzero symmetric invariant bilinear forms on vertex operator algebras and an analogue of the Cartan criterion for semi-simplicity are presented.
Journal ArticleDOI
Voronoi regions of lattices, second moments of polytopes, and quantization
John H. Conway,Neil J. A. Sloane +1 more
TL;DR: The answers to the squared distance questions and a description of the Voronoi (or nearest neighbor) regions of these lattices have applications to quantization and to the design of signals for the Gaussian channel.
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Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
Patrick Dehornoy,Luis Paris +1 more
TL;DR: In this article, it was shown that Garside groups are geodesically fully biautomatic, and that the language of normal forms for Gaussian groups is regular, symmetric, and geodesic.
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Local Systems of Vertex Operators, Vertex Superalgebras and Modules
TL;DR: The notion of vertex operator superalgebras was introduced in this paper, where it was shown that any local system of vertex operators on a super vector space has a natural vertex (super)algebra structure with $M$ as a module.
References
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Journal ArticleDOI
Local systems of vertex operators, vertex superalgebras and modules
TL;DR: In this article, it was shown that the vertex operator superalgebra V has a vertex (super)algebra structure with M as a module, and for a vertex operator V, giving a V-module M is equivalent to giving a vertex operators homomorphism from V to some local system of vertex operators on a vector space.
Journal ArticleDOI
Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality
TL;DR: The Wilson-t Hooft operator as mentioned in this paper is a topologically nontrivial operator that is localized on a straight line, creates electric and magnetic flux, and in the UV limit breaks the conformal invariance in the minimal possible way.
Journal ArticleDOI
Symmetric invariant bilinear forms on vertex operator algebras
TL;DR: In this paper, a criterion for determining the existence of nonzero symmetric invariant bilinear forms on vertex operator algebras and an analogue of the Cartan criterion for semi-simplicity are presented.
Journal ArticleDOI
Voronoi regions of lattices, second moments of polytopes, and quantization
John H. Conway,Neil J. A. Sloane +1 more
TL;DR: The answers to the squared distance questions and a description of the Voronoi (or nearest neighbor) regions of these lattices have applications to quantization and to the design of signals for the Gaussian channel.
Introduction to Shimura Varieties
TL;DR: In this article, an introduction to the theory of Shimura varieties is given, or, in other words, to the arithmetic theory of automorphic functions and holomorphic automomorphic forms.