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arXiv · 1410.4455

Rigged Configurations and Cylindric Loop Schur Functions

Thomas Lam·Pavlo Pylyavskyy·Reiho Sakamoto
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Abstract

Rigged configurations are known to provide action-angle variables for remarkable discrete dynamical systems known as box-ball systems. We conjecture an explicit piecewise-linear formula to obtain the shapes of a rigged configuration from a tensor product of one-row crystals. We introduce cylindric loop Schur functions and show that they are invariants of the geometric R-matrix. Our piecewise-linear formula is obtained as the tropicalization of ratios of cylindric loop Schur functions. We prove our conjecture for the first shape of a rigged configuration, thus giving a piecewise-linear formula for the lengths of the solitons of a box-ball system.

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BibTeXRIS

Thomas Lam, Pavlo Pylyavskyy, Reiho Sakamoto. 2014-10-16. Rigged Configurations and Cylindric Loop Schur Functions. https://doi.org/10.4171/aihpd/61

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