Trajectories of jeu de taquin and second class particles

• Applicant: Professor Dr. Piotr Sniady
• Subject Area: Mathematics
• Term: from 2012 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 219922243

We study an infinite version of Schützenberger's „jeu de taquin“, which is one of the key tools of the representation theory of the symmetric groups, closely related to Robinson-Schensted-Knuth (RSK) algorithm and Littlewood-Richardson rule. In the infinite setup which we study, jeu de taquin becomes a transformation on the set of infinite Young tableaux and thus is useful to the harmonic analysis on the infinite symmetric group and its representation theory. This topic is closely related to exclusion processes in mathematical physics, where jeu de taquin corresponds to the notion of second class particles. We investigate the statistical properties of the trajectories of jeu de taquin / trajectories of second class particles and we study their applications to harmonic analysis on the infinite symmetric group. Keywords: asymptotic representation theory, harmonic analysis, representations of finite and infinite symmetric groups, Young diagrams, exclusion processes.

• DFG Programme: Research Grants