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

Role of the plasma-electrode bias and the transverse magnetic field upon H- ion extraction in the negative ion source

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Factorization, reduction and embedding in integrable cellular automata

Factorized dynamics in soliton cellular automata with quantum group symmetry is identified with a motion of particles and anti-particles exhibiting pair creation and annihilation. An embedding scheme is presented showing that the D^{(1)}_n-automaton contains, as certain subsectors, the box-ball systems and all the other automata associated with the crystal bases of non-exceptional affine Lie algebras. The results extend the earlier ones to higher representations by a certain reduction and to a wider class of boundary conditions.Comment: LaTeX2e, 20 page

Combinatorial Bethe ansatz and ultradiscrete Riemann theta function with rational characteristics

The U_q(\hat{sl}_2) vertex model at q=0 with periodic boundary condition is an integrable cellular automaton in one-dimension. By the combinatorial Bethe ansatz, the initial value problem is solved for arbitrary states in terms of an ultradiscrete analogue of the Riemann theta function with rational characteristics.Comment: 9 page

Syntheses of some 1-(alpha-hydroxybenzyl)thieno[3,4-b]indolizine derivatives and their unexpected condensation reactions

Some ethyl 3-(benzyl or methylthio)-1-(alpha-hydroxybenzyl)- thieno[3,4-b]indolizine-9-carboxylates were prepared by the reduction of the corresponding 1-benzoyl derivatives with sodium borohydride. These compounds were considerably unstable and their treatment with acetic acid afforded the unexpected condensation products.ArticleHETEROCYCLES. 65(7): 1557-1560 (2005)journal articl

The A^{(1)}_M automata related to crystals of symmetric tensors

A soliton cellular automaton associated with crystals of symmetric tensor representations of the quantum affine algebra U'_q(A^{(1)}_M) is introduced. It is a crystal theoretic formulation of the generalized box-ball system in which capacities of boxes and carriers are arbitrary and inhomogeneous. Scattering matrices of two solitons coincide with the combinatorial R matrices of U'_q(A^{(1)}_{M-1}). A piecewise linear evolution equation of the automaton is identified with an ultradiscrete limit of the nonautonomous discrete KP equation. A class of N soliton solutions is obtained through the ultradiscretization of soliton solutions of the latter.Comment: 45 pages, latex2e, 2 figure

Critical RSOS and Minimal Models II: Building Representations of the Virasoro Algebra and Fields

We consider sl(2) minimal conformal field theories and the dual parafermion models. Guided by results for the critical A_L Restricted Solid-on-Solid (RSOS) models and its Virasoro modules expressed in terms of paths, we propose a general level-by-level algorithm to build matrix representations of the Virasoro generators and chiral vertex operators (CVOs). We implement our scheme for the critical Ising, tricritical Ising, 3-state Potts and Yang-Lee theories on a cylinder and confirm that it is consistent with the known two-point functions for the CVOs and energy-momentum tensor. Our algorithm employs a distinguished basis which we call the L_1-basis. We relate the states of this canonical basis level-by-level to orthonormalized Virasoro states