Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case

In proving the Fermionic formulae, combinatorial bijection called the Kerov--Kirillov--Reshetikhin (KKR) bijection plays the central role. It is a bijection between the set of highest paths and the set of rigged configurations. In this paper, we give a proof of crystal theoretic reformulation of the KKR bijection. It is the main claim of Part I (math.QA/0601630) written by A. Kuniba, M. Okado, T. Takagi, Y. Yamada, and the author. The proof is given by introducing a structure of affine combinatorial $R$ matrices on rigged configurations.Comment: 45 pages, version for publication. Introduction revised, more explanations added to the main tex

HSPH1 (heat shock 105kDa/110kDa protein 1)

Review on HSPH1 (heat shock 105kDa/110kDa protein 1), with data on DNA, on the protein encoded, and where the gene is implicated

Creation of ballot sequences in a periodic cellular automaton

Motivated by an attempt to develop a method for solving initial value problems in a class of one dimensional periodic cellular automata (CA) associated with crystal bases and soliton equations, we consider a generalization of a simple proposition in elementary mathematics. The original proposition says that any sequence of letters 1 and 2, having no less 1's than 2's, can be changed into a ballot sequence via cyclic shifts only. We generalize it to treat sequences of cells of common capacity s > 1, each of them containing consecutive 2's (left) and 1's (right), and show that these sequences can be changed into a ballot sequence via two manipulations, cyclic and "quasi-cyclic" shifts. The latter is a new CA rule and we find that various kink-like structures are traveling along the system like particles under the time evolution of this rule.Comment: 31 pages. Section 1 changed and section 5 adde

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

Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations

There are two distinct approaches to the study of initial value problem of the periodic box-ball systems. One way is the rigged configuration approach due to Kuniba--Takagi--Takenouchi and another way is the 10-elimination approach due to Mada--Idzumi--Tokihiro. In this paper, we describe precisely interrelations between these two approaches.Comment: 16 pages, final version, minor revisio

Difference L operators and a Casorati determinant solution to the T-system for twisted quantum affine algebras

We propose factorized difference operators L(u) associated with the twisted quantum affine algebras U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}), U_{q}(D^{(2)}_{n+1}),U_{q}(D^{(3)}_{4}). These operators are shown to be annihilated by a screening operator. Based on a basis of the solutions of the difference equation L(u)w(u)=0, we also construct a Casorati determinant solution to the T-system for U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}).Comment: 15 page