Soliton cellular automata constructed from a Uq(Dn[1])-crystal Bn,1 and kirillov-reshetikhin type bijection for Uq(E6[1])-crystal B6,1

• 第一著者: Mohamad, Mahathir
• フォーマット: 学位論文
• 言語: 英語
• 出版事項: 2012
• 主題: QA150-272.5 Algebra
• オンライン･アクセス: http://eprints.uthm.edu.my/2542/

In part 1 we study a class of cellular automata associated with the Kirillov-Reshetikhin crystal B n;1 of type D (1) n . They have a commuting family of time evolutions and solitons of length l are labeled by U q (A (1) n1 )-crystal B 2;l A . The scattering rule of two solitons of lengths l 1 and l 2 (l 1 > l ) including the phase shift is identified with the combinatorial R-matrix for the U q 2 (A (1) n1 )-crystal B 2;l A 2 B 2;l A 1 . In part 2 we consider the Kirrilov-Reshetikhin crystal B 6;1 for the exceptional affine type E . We will give a conjecture on a statistic-preserving bijection between the highest weight paths consisting of B 6;1 and the corresponding rigged configuration. The algorithm only uses the structure of the crystal graph, hence could also be applied for other exceptional types. Our B 6;1 has a different algorithm compared our B 1;1 because we must consider the element Ø, unique element in the highest weight crystal of weight 0, in the crystal graph. We will give many examples supporting the conjecture. (1) 6