Vertex Algebras
Mostrando 1-11 de 11 artigos, teses e dissertações.
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1. Vertex structures in representation theory of Lie algebras / Estruturas de Vertex em teoria de representações de álgebras de Lie
Following the results of [BBFK11], our work starts analyzing (for bsl(n;C)) if we can obtain J-imaginary Verma modules using similar representations used by Cox in [Cox05]. We did it for n = 2 and after, for the general case. The next step was the study of J-intermediate Wakimoto modules, following the ideas of [CF04] and [CF05]. To finish, for affine sl(2;C
IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia. Publicado em: 04/05/2012
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2. Geometric invariant theory and representations of quivers / Teoria geometrica dos invariantes e representações de quivers
This thesis is divided into two parts. ln the first part we present the main ideas and tools of Geometric lnvariant Theory, which is concerned with the following problem: ls it possible to give an algebraic structure to the quotient of an algebraic variety by the action of an algebraic group? Qne of the most important results says that an algebraic quotient
Publicado em: 2006
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3. Vertex representations of quantum affine algebras
We construct vertex representations of quantum affine algebras of ADE type, which were first introduced in greater generality by Drinfeld and Jimbo. The limiting special case of our construction is the untwisted vertex representation of affine Lie algebras of Frenkel-Kac and Segal. Our representation is given by means of a new type of vertex operator corresp
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4. Geometric interpretation of vertex operator algebras.
In this paper, Vafa's approach to the formulation of conformal field theories is combined with the formal calculus developed in Frenkel, Lepowsky, and Meurman's work on the vertex operator construction of the Monster to give a geometric definition of vertex operator algebras. The main result announced is the equivalence between this definition and the algebr
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5. Calculus of twisted vertex operators
Starting from an arbitrary isometry of an arbitrary even lattice, twisted and shifted vertex operators are introduced. Under commutators, these operators provide realizations of twisted affine Lie algebras. This construction, generalizing a number of known ones, is based on a self-contained “calculus.”
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6. Vertex algebras, Kac-Moody algebras, and the Monster
It is known that the adjoint representation of any Kac-Moody algebra A can be identified with a subquotient of a certain Fock space representation constructed from the root lattice of A. I define a product on the whole of the Fock space that restricts to the Lie algebra product on this subquotient. This product (together with a infinite number of other produ
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7. From the representation theory of vertex operator algebras to modular tensor categories in conformal field theory
National Academy of Sciences.
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8. Algebraic orbifold conformal field theories
The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown tha
The National Academy of Sciences.
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9. A new family of algebras underlying the Rogers-Ramanujan identities and generalizations
The classical Rogers-Ramanujan identities have been interpreted by Lepowsky-Milne and the present authors in terms of the representation theory of the Euclidean Kac-Moody Lie algebra A1(1). Also, the present authors have introduced certain “vertex” differential operators providing a construction of A1(1) on its basic module, and Kac, Kazhdan, and we have
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10. Vertex operator algebras, the Verlinde conjecture, and modular tensor categories
Let V be a simple vertex operator algebra satisfying the following conditions: (i) V(n) = 0 for n < 0, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}V_{0}={\mathbb{C}}1\end{equat
National Academy of Sciences.
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11. A natural representation of the Fischer-Griess Monster with the modular function J as character
We announce the construction of an irreducible graded module V for an “affine” commutative nonassociative algebra [unk]. This algebra is an “affinization” of a slight variant [unk] of the commutative nonassociative algebra B defined by Griess in his construction of the Monster sporadic group F1. The character of V is given by the modular function J(q