Soliton cellular automaton associated with D-n((1))-crystal B-2,B-s

Author(s)

Misra, Kailash C. ^[1] ; Wilson, Evan A. ^{[2, 1]}

Affiliation

^[1] N Carolina State Univ, Dept Math, Raleigh, NC 27695 - USA

^[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Physics; v. 54, n. 4 APR 2013.
• Web of Science Citations: 2

Abstract

A solvable vertex model in ferromagnetic regime gives rise to a soliton cellular automaton which is a discrete dynamical system in which site variables take on values in a finite set. We study the scattering of a class of soliton cellular automata associated with the U-q(D-n((1)))-perfect crystal B-2,B- s. We calculate the combinatorial R matrix for all elements of B-2,B- s circle times B-2,B- 1. In particular, we show that the scattering rule for our soliton cellular automaton can be identified with the combinatorial R matrix for U-q(A(1)((1))) circle plus U-q (D-n-2((1)))-crystals. (C) 2013 AIP Publishing LLC. (AU)

• FAPESP's process: 11/12079-5 - Representations of Kac-Moody Algebras and quantum groups
• Grantee: Evan Andrew Wilson
• Support Opportunities: Scholarships in Brazil - Post-Doctoral