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Doctoral Thesis
DOI
10.11606/T.45.2017.tde-05122017-105106
Document
Author
Full name
German Alonso Benitez Monsalve
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2016
Supervisor
Committee
Futorny, Vyacheslav (President)
Bekkert, Viktor
Calixto, Lucas Henrique
Gonzalez, Cristian Andres Ortiz
Jardim, Marcos Benevenuto
Title in Portuguese
Variedades de Gelfand-Tsetlin
Keywords in Portuguese
Dimensão
Equidimensionalidade
Gelfand-Tsetlin
Kostant-Wallach
Variedades algébricas
Yangians
Abstract in Portuguese
Serge Ovsienko provou que a variedade de Gelfand-Tsetlin para gl(n) é equidimensional (i.e., todas suas componentes irredutíveis têm a mesma dimensão) com dimensão n(n-1)/2. Este resultado é conhecido como "Teorema de Ovsienko" e tem importantes consequências na Teoria de Representacões de Álgebras. Neste trabalho, provamos uma versão fraca do Teorema de Ovsienko para gl(n) e estendemos tal versão fraca a uma estrutura que tem como caso particular gl(3), esse é o caso do grupo quântico Yangian Yp(gl(3)) de nível p. Além disso, o Teorema de Ovsienko também tem consequências na Geometria Simplética, especificamente na equidimensionalidade das fibras em uma projeção da aplicação de Kostant-Wallach. Neste trabalho apresentamos a generalização deste resultado.
Title in English
Gelfand-Tsetlin varieties
Keywords in English
Algebraic varieties
Dimension
Equidimensionality
Gelfand-Tsetlin
Kostant-Wallach
Yangians
Abstract in English
Serge Ovsienko proved that the Gelfand-Tsetlin variety for gl(n) is equidimensional (i.e., all its irreducible components have the same dimension) with dimension n(n-1)/2. This result is known as "Ovsienko's Theorem" and it has important consequences in Representation Theory of Algebras. In this work, we prove a weak version of Ovsienko's Theorem for gl(n) and we extend that weak version to a structure which has as particular case gl(3), this case is the quantum group level p Yangian Yp(gl(3)). Moreover, the theorem of Ovsienko also has consequences in Symplectic Geometry, more concretely in the equidimensionality of the fibers in a projection of the Kostant-Wallach map. In this work we will present the generalization of that result.
 
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Tese.pdf (742.42 Kbytes)
Publishing Date
2017-12-05
 
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