PORTUGUESE

Grafo da ramificação para representações irredutíveis de grupos simétricos: isomorfismo com o Grafo de Young [Master thesis]

By Tânia Sofia Zaragoza Cotrim Silva

Book information

Publisher
Universidade de Lisboa
Year
2014
Language
portuguese
Format
PDF
Filesize
939 kB (961413 bytes)
Pages
90\90
Time added
2016-11-15 07:16:21

Description

In this paper we prove that the branching graph, built through the equivalence classesof irreducible representations of S n and the respective irreducible components of therestrictions to S n−1 , coincides, both in vertices as in paths, with the Young graph,composed of Young diagrams of partitions of n and the respective diagrams that areobtained when subtracted a removable box. To achieve this goal we resorted to partic-ular elements of the symmetric group algebra and indexed the paths of the branchinggraph to a set of Z n vectors, to which we could also index the paths of Young graph,using, in this case, Young tableaux.Keywords: representation, symmetric group, Young diagram, Gelfand-Zetlin algebra,Gelfand-Zetlin basis, Jucys-Murphy element

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