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arXiv · 1001.1813

Generalized energies and integrable D^{(1)}_n cellular automaton

Atsuo Kuniba·Reiho Sakamoto·Yasuhiko Yamada
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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.

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Atsuo Kuniba, Reiho Sakamoto, Yasuhiko Yamada. 2010-12-09. Generalized energies and integrable D^{(1)}_n cellular automaton. https://doi.org/10.1142/9789814324373_0012

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