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4 papers · 1 filter
Differential equations for the closed geometric crystal chains
Taichiro Takagi
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…
Geometric lifting of the integrable cellular automata with periodic boundary conditions
Taichiro Takagi, Takuma Yoshikawa
Inspired by G. Frieden's recent work on the geometric R-matrix for affine type A crystal associated with rectangular shaped Young tableaux, we propose a method to construct a novel…
Commuting Time Evolutions in the Tropical Periodic Toda Lattice
Taichiro Takagi
The tropical (ultradiscrete) periodic Toda lattice is a dynamical system derived from a time-discretized version of the periodic Toda lattice through a limiting procedure called tr…
Fermionic partition functions for a periodic soliton cellular automaton
Atsuo Kuniba, Taichiro Takagi
Fermionic formulas in combinatorial Bethe ansatz consist of sums of products of q-binomial coefficients. There exist refinements without a sum that are known to yield partition fun…