484 research outputs found
A crystal theoretic method for finding rigged configurations from paths
The Kerov--Kirillov--Reshetikhin (KKR) bijection gives one to one
correspondences between the set of highest paths and the set of rigged
configurations. In this paper, we give a crystal theoretic reformulation of the
KKR map from the paths to rigged configurations, using the combinatorial R and
energy functions. This formalism provides tool for analysis of the periodic
box-ball systems.Comment: 24 pages, version for publicatio
Bethe ansatz at q=0 and periodic box-ball systems
A class of periodic soliton cellular automata is introduced associated with
crystals of non-exceptional quantum affine algebras. Based on the Bethe ansatz
at q=0, we propose explicit formulas for the dynamical period and the size of
certain orbits under the time evolution in A^{(1)}_n case.Comment: 12 pages, Introduction expanded, Summary added and minor
modifications mad
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