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arXiv · 2203.12325

Differential equations for the closed geometric crystal chains

Taichiro Takagi
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Abstract

We present two types of systems of differential equations that can be derived from a set of discrete integrable systems which we call the closed geometric crystal chains. One is a kind of extended Lotka-Volterra systems, and the other seems to be generally new but reduces to a previously known system in a special case. Both equations have Lax representations associated with what are known as the loop elementary symmetric functions, which were originally introduced to describe products of affine type A geometric crystals for symmetric tensor representations. Examples of the derivations of the continuous time Lax equations from a discrete time one are described in detail, where a novel method of taking a continuum limit by assuming asymptotic behaviors of the eigenvalues of the Lax matrix in Puiseux series expansions is used.

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Taichiro Takagi. 2022-03-23. Differential equations for the closed geometric crystal chains. https://doi.org/10.1088/1751-8121%2Fac909a

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