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

In this paper we prove that the branching graph, built through the equivalence classes
of irreducible representations of S n and the respective irreducible components of the
restrictions 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 are
obtained 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 branching
graph 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