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Seminars

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
Place
Ito campus, Faculty of Mathematics building, Room 122
Object person
 
Speaker
Tullio Ceccherini-Silberstein (University of Sannio)

*臨時組合せ数学セミナー
ABSTRACT: In this talk, I would like to describe the representation 
theory
of the symmetric groups along the new lines developed by several 
authors,
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 
authors.
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
functions;
(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.