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Master Thesis

Tours de groupes et diagrammes de Bratteli

Abstract : A new approach of the representation theory of the symmetric group has been developped by Okounkov et Vershik; it provides a different point of view on the subject compared to the "traditional" approaches. Moreover it intends to be generalizable to other chains of groups and algebras such as the other series of finite Coxeter groups, or the local and stationary towers of algebras. In this report we remind the usual presentation of the symmetric group and outline the new approach of its representation theory. Then we recall the definition of a local and stationary tower of algebras, of Bratteli diagram and of what is called Gelfand-Tsetlin basis and Gelfand-Tsetlin algebra in the new approach. We attempted to generalize this new approach to the chain of the alternating groups. For this purpose we study two known presentations of the alternating group, and give a new one which supplies the chain of the alternating groups with a structure of a local and stationary tower; in each case we realize the Coxeter-Todd algorithm and give a normal form for the elements of the group. We also begin the search for analogues of Jucys-Murphy elements for the alternating groups.
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https://dumas.ccsd.cnrs.fr/dumas-00490056
Contributor : Oleg Ogievetsky <>
Submitted on : Monday, June 7, 2010 - 6:20:56 PM
Last modification on : Tuesday, March 30, 2021 - 3:17:12 AM
Long-term archiving on: : Friday, October 19, 2012 - 3:40:26 PM

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  • HAL Id : dumas-00490056, version 1

Citation

Loïc Poulain d'Andecy. Tours de groupes et diagrammes de Bratteli. Physique mathématique [math-ph]. 2008. ⟨dumas-00490056⟩

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