ICTS:30049

Video URL

Skew column RSK dynamics and the box and ball system

Skew column RSK dynamics and the box and ball system

(2024). Skew column RSK dynamics and the box and ball system. SciVideos. https://youtube.com/live/7Hy9jFTtIGY

Skew column RSK dynamics and the box and ball system. SciVideos, Oct. 30, 2024, https://youtube.com/live/7Hy9jFTtIGY 

          @misc{ scivideos_ICTS:30049,
            doi = {},
            url = {https://youtube.com/live/7Hy9jFTtIGY},
            author = {},
            keywords = {},
            language = {en},
            title = {Skew column RSK dynamics and the box and ball system},
            publisher = {},
            year = {2024},
            month = {oct},
            note = {ICTS:30049 see, \url{https://scivideos.org/icts-tifr/30049}}
          }
Takashi Imamura
Talk numberICTS:30049
Source RepositoryICTS-TIFR
Source EventDiscrete integrable systems: difference equations, cluster algebras and probabi…
Collection

Abstract

In our previous study (TI-Mucciconi-Sasamoto, Forum of Mathematics, Pi 11(e27) 1-101,2023) we introduced a deterministic time evolution of a pair of skew semistandard Young tableaux called the skew RSK dynamics.

In this talk we introduce a variant based on the column bumping in the RSK correspondence, which we call the column skew RSK dynamics. Utilizing (bi) crystal structure in the pair of skew tableaux, we show that the column skew RSK dynamics can be mapped to the single species box and ball system (BBS).  Using the mapping we obtain a relation between restricted Cauchy sums about the modified Hall-Littlewood polynomials and the skew Schur polynomials. This talk is based on the joint work with Matteo Mucciconi, Tomohiro Sasamoto and Travis Scrimshaw.