分野別セミナー

＊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.