Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Nonlinear Sciences > Cellular Automata and Lattice Gases

arXiv:nlin/0310002 (nlin)
[Submitted on 3 Oct 2003]

Title:Factorization, reduction and embedding in integrable cellular automata

Authors:A. Kuniba, T. Takagi, A. Takenouchi
View PDF
Abstract: 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.
Comments: LaTeX2e, 20 pages
Subjects: Cellular Automata and Lattice Gases (nlin.CG); Quantum Algebra (math.QA); Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:nlin/0310002 [nlin.CG]
  (or arXiv:nlin/0310002v1 [nlin.CG] for this version)
  https://doi.org/10.48550/arXiv.nlin/0310002
Journal reference: J. of Phys. A: Math. Gen. 37 (2004) 1691-1709
Related DOI: https://doi.org/10.1088/0305-4470/37/5/015

Submission history

From: Atsuo Kuniba [view email]
[v1] Fri, 3 Oct 2003 09:05:52 UTC (24 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
nlin.CG
< prev   |   next >
new | recent | 2003-10

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)