Soliton Cellular Automata constructed from a Uq(Dn(1)n)-Crystal Bn,1 and Kirillov-Reshetikhin type bijection for Uq(E6(1))-Crystal B6,1

Mohamad, Mahathir (2012) Soliton Cellular Automata constructed from a Uq(Dn(1)n)-Crystal Bn,1 and Kirillov-Reshetikhin type bijection for Uq(E6(1))-Crystal B6,1. PhD thesis, Osaka University.

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Abstract

In part 1 we study a class of cellular automata associated with the Kirillov-Reshetikhin crystal Bn;1 of type D(1) n . They have a commuting family of time evolutions and solitons of length l are labeled by Uq(A(1) n..1)-crystal B2;l A . The scattering rule of two solitons of lengths l1 and l2 (l1 > l2) including the phase shift is identi�ed with the combinatorial R-matrix for the Uq(A(1) n..1)-crystal B2;l2 A B2;l1 A . In part 2 we consider the Kirrilov-Reshetikhin crystal B6;1 for the exceptional a�ne type E(1) 6 . We will give a conjecture on a statistic-preserving bijection between the highest weight paths consisting of B6;1 and the corresponding rigged con�guration. The algorithm only uses the structure of the crystal graph, hence could also be applied for other exceptional types. Our B6;1 has a di�erent algorithm compared our B1;1 because we must consider the element �, unique element in the highest weight crystal of weight 0, in the crystal graph. We will give many examples supporting the conjecture.

Item Type:Thesis (PhD)
Subjects:T Technology > T Technology (General)
ID Code:2694
Deposited By:Normajihan Abd. Rahman
Deposited On:28 Aug 2012 16:52
Last Modified:28 Aug 2012 16:52

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