359 research outputs found
Simple Algorithm for Factorized Dynamics of g_n-Automaton
We present an elementary algorithm for the dynamics of recently introduced
soliton cellular automata associated with quantum affine algebra U_q(g_n) at
q=0. For g_n = A^{(1)}_n, the rule reproduces the ball-moving algorithm in
Takahashi-Satsuma's box-ball system. For non-exceptional g_n other than
A^{(1)}_n, it is described as a motion of particles and anti-particles which
undergo pair-annihilation and creation through a neutral bound state. The
algorithm is formulated without using representation theory nor crystal basis
theory.Comment: LaTex2e 9 pages, no figure. For proceedings of SIDE IV conferenc
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
matrices on rigged configurations.Comment: 45 pages, version for publication. Introduction revised, more
explanations added to the main tex
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
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
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
Integrated Modeling of Negative Hydrogen (H?/D?) Ion Production, Extraction and Acceleration in a Large Negative Ion Source for Neutral Beam Injection System
Integrated Modeling of Negative Hydrogen (H?/D?) Ion Production, Extraction and Acceleration in a Large Negative Ion Source for Neutral Beam Injection System
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
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