Affine crystal structure on rigged configurations of type D_n^(1)

Extending the work arXiv:math/0508107, we introduce the affine crystal action on rigged configurations which is isomorphic to the Kirillov-Reshetikhin crystal B^{r,s} of type D_n^(1) for any r,s. We also introduce a representation of B^{r,s} (r not equal to n-1,n) in terms of tableaux of rectangular shape r x s, which we coin Kirillov-Reshetikhin tableaux (using a non-trivial analogue of the type A column splitting procedure) to construct a bijection between elements of a tensor product of Kirillov-Reshetikhin crystals and rigged configurations.Comment: 26 pages, 3 figures. (v3) corrections in the proof reading. (v2) 26 pages; examples added; introduction revised; final version. (v1) 24 page

Crystals for Demazure Modules of Classical Affine Lie Algebras

We study, in the path realization, crystals for Demazure modules of affine Lie algebras of types $A^{(1)}_n,B^{(1)}_n,C^{(1)}_n,D^{(1)}_n, A^{(2)}_{2n-1},A^{(2)}_{2n}, and D^{(2)}_{n+1}$. We find a special sequence of affine Weyl group elements for the selected perfect crystal, and show if the highest weight is l\La_0, the Demazure crystal has a remarkably simple structure.Comment: Latex, 28 page

Soliton cellular automaton associated with G2(1)G_2^{(1)} crystal base

We calculate the combinatorial $R$ matrix for all elements of $\mathcal{B}_l\otimes \mathcal{B}_1$ where $\mathcal{B}_l$ denotes the $G_2^{(1)}$-perfect crystal of level $l$, and then study the soliton cellular automaton constructed from it. The solitons of length $l$ are identified with elements of the $A_1^{(1)}$-crystal $\tilde{\mathcal{B}}_{3l}$. The scattering rule for our soliton cellular automaton is identified with the combinatorial $R$ matrix for $A_1^{(1)}$-crystals

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