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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2012.tde-07092012-173756
Document
Author
Full name
Renato Alessandro Martins
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Futorny, Vyacheslav (President)
Grantcharov, Dimitar
Guzzo Junior, Henrique
Heluani, Reimundo
Kochloukov, Plamen Emilov
Title in Portuguese
Estruturas de Vertex em teoria de representações de álgebras de Lie
Keywords in Portuguese
álgebras de Vertex.
módulos de Verma clássicos
módulos de Verma imaginários
módulos de Verma J-imaginários
módulos intermediários de Wakimoto
módulos J-intermediários de Wakimoto
Abstract in Portuguese
Motivados pelos resultados do artigo [BBFK11], nosso trabalho começa analisando, no caso da álgebra de Lie afim sl(n;C), a possibilidade de se obter módulos de Verma J-imaginários, via representações análogas às feitas por Cox em [Cox05]. Inicialmente consideramos, por simplicidade, n = 2 e, só então, analisamos o caso geral. Depois, de modo análogo, estudamos os artigos [CF04] e [CF05] com o intuito de obter módulos J-intermediários de Wakimoto. Finalmente imbutimos, no caso n = 2, uma ação de álgebra de Virasoro nos módulos imaginários de Wakimoto, utilizando-nos do resultado exposto em [EFK98], em que tal problema é abordado para o caso dos módulos de Verma. Desta forma, obtemos equações análogas às de Knizhnik-Zamolodchikov (equações KZ) para os módulos imaginários de Wakimoto.
Title in English
Vertex structures in representation theory of Lie algebras
Keywords in English
classical Verma modules
imaginary Verma modules
intermediate Wakimoto modules
J-imaginary Verma modules
J-intermediate Wakimoto modules
Vertex algebras.
Abstract in English
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), we defined an action of Virasoro algebra on the imaginary Wakimoto modules following [EFK98] and we obtained an analogue of the KZ-equations for imaginary Wakimoto modules.
 
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Publishing Date
2012-09-10
 
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