Combinatorics of asymptotic representation theory

Details Combinatorics of asymptotic representation theory Combinatorics of asymptotic representation theory

2012-03-29

arxiv.org/abs/1203.6509v1

Mathematics

Combinatorics

Overview article for general mathematical audience, proceedings of European Congress of Mathematics 2012

Scientific paper

The representation theory of the symmetric groups S_n is intimately related to combinatorics: combinatorial objects such as Young tableaux and combinatorial algorithms such as Murnaghan-Nakayama rule. In the limit as n tends to infinity, the structure of these combinatorial objects and algorithms becomes complicated and it is hard to extract from them some meaningful answers to asymptotic questions. In order to overcome these difficulties, a kind of dual combinatorics of the representation theory of the symmetric groups was initiated in 1990s. We will concentrate on one of its highlights: Kerov polynomials which express characters in terms of, so called, free cumulants.

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