Geodesic
Rigged configurations and cylindric loop Schur functions
Annales de l’Institut Henri Poincaré D, Tome 5 (2018) no. 4, pp. 513-555

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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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DOI : 10.4171/aihpd/61
Classification : 05-XX, 37-XX, 70-XX
Keywords: Rigged configuration, discrete soliton, box ball system, tropicalization, loop schur functions 
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     title = {Rigged configurations and cylindric loop {Schur} functions},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {513--555},
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     doi = {10.4171/aihpd/61},
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     language = {en},
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Lam, Thomas; Pylyavskyy, Pavlo; Sakamoto, Reiho. Rigged configurations and cylindric loop Schur functions. Annales de l’Institut Henri Poincaré D, Tome 5 (2018) no. 4, pp. 513-555. doi: 10.4171/aihpd/61

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