Yang-Baxter maps: dynamical point of view
Quantum Algebra
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
A review of some recent results on the dynamical theory of the Yang-Baxter maps (also known as set-theoretical solutions to the quantum Yang-Baxter equation) is given. The central question is the integrability of the transfer dynamics. The relations with matrix factorisations, matrix KdV solitons, Poisson Lie groups, geometric crystals and tropical combinatorics are discussed and demonstrated on several concrete examples.
Cite
@article{arxiv.math/0612814,
title = {Yang-Baxter maps: dynamical point of view},
author = {A. P. Veselov},
journal= {arXiv preprint arXiv:math/0612814},
year = {2007}
}
Comments
24 pages. Extended version of lectures given at the meeting "Combinatorial Aspect of Integrable Systems" (RIMS, Kyoto, July 2004)