{"paper":{"title":"Soliton cellular automaton associated with $D_n^{(1)}$-crystal $B^{2,s}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Evan A. Wilson, Kailash C. Misra","submitted_at":"2012-09-20T15:12:06Z","abstract_excerpt":"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 $B^{2,s}$. We calculate the combinatorial $R$ matrix for all elements of $B^{2,s} \\otimes B^{2,1}$. In particular, we show that the scattering rule for our soliton cellular automaton can be identified with the combinatorial $R$ matrix for $U_q(A_1^{(1)}) \\oplus U_q(D_{n-2}^{(1)})$-crystals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4558","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}