Generalized energies and integrable D^{(1)}_n cellular automaton
Quantum Algebra
2017-08-23 v2 Combinatorics
Abstract
We introduce generalized energies for a class of U_q(D^{(1)}_n) crystals by using the piecewise linear functions that are building blocks of the combinatorial R. They include the conventional energy in the theory of affine crystals as a special case. It is shown that the generalized energies count the particles and anti-particles in a quadrant of the two dimensional lattice generated by time evolutions of an integrable D^{(1)}_n cellular automaton. Explicit formulas are conjectured for some of them in the form of ultradiscrete tau functions.
Keywords
Cite
@article{arxiv.1001.1813,
title = {Generalized energies and integrable D^{(1)}_n cellular automaton},
author = {Atsuo Kuniba and Reiho Sakamoto and Yasuhiko Yamada},
journal= {arXiv preprint arXiv:1001.1813},
year = {2017}
}
Comments
For proceedings of "Infinite Analysis 09: New Trends in Quantum Integrable Systems"