Skew RSK dynamics and affine crystal

Tomohiro Sasamoto (Tokyo Institute of Technology)

Tuesday 16th January 16:00-17:00 Maths 311B

Abstract

We explain various properties and applications of the skew RSK dynamics, which we introduced as a time evolution for a pair of skew Young tableaux (P,Q) [1]. The dynamics exhibits solitonic behaviors similar to box ball systems (BBS).  Associated affine crystal structure allows to give a bijective proof of the Cauchy identity for the $q$-Whittaker polynomials. Its refinement provides a connection between Kardar-Parisi-Zhang(KPZ) models and free fermions at finite temperature[2]. 

 

[1] T. Imamura, M. Mucciconi, T. Sasamoto, Skew RSK dynamics: Greene invariants, affine crystals and applications to $q$-Whittaker polynomials, Forum of Mathematics, Pi (2023), e27 1–101 (arXiv: 2106.11922). 

[2] T. Imamura, M. Mucciconi, T. Sasamoto, Solvable models in the KPZ class: approach through periodic and free boundary Schur measures, (arXiv: 2204.08420)  

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