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On the Okounkov-Vershik approach to the representation theory of the symmetric groups

Hold Date
2010-02-09 15:00〜2010-02-09 16:30
Ito campus, Faculty of Mathematics building, Room 122
Object person
Tullio Ceccherini-Silberstein (University of Sannio)

ABSTRACT: In this talk, I would like to describe the representation 
of the symmetric groups along the new lines developed by several 
in particular by A.M. Vershik, G.I. Olshanskii and A. Okounkov.
The tools/ingredients of this new approach are either completely new,
or were not fully understood in their whole importance by previous 
I'll try to analyze such tools/ingredients which consist of:
(i) the algebras of conjugacy-invariant functions, the algebras of
bi-$K$-invariant functions, the Gelfand pairs and their spherical
(ii) the Gelfand-Tsetlin algebras and their corresponding bases;
(iii)  the branching diagrams, the associated posets and the content 
of a tableau;
(iv) the Young-Jucys-Murphy elements and their spectral analysis;
(v) the characters of the symmetric group viewed as spherical functions.