Epsilon systems on geometric crystals of type \(A_n\) (Q970339)

In the theory of crystal bases, the piecewise-linear functions \(\epsilon_i\) and \(\phi_i\) play many crucial roles. There exist counterparts for geometric crystals which are rational functions with several nice properties. Higher objects of the epsilon functions wrre also introduced. The article under review defines further higher objects, namely, the ``epsilon system'' for type \(A_n\) and reveals its basic properties on product structures, invariance under the action of tropical R maps, etc.