Scattering rule in soliton cellular automaton associated with crystal base of Uq(D4(3))

DOI10.1063/1.2721347zbMath1112.81060arXivmath/0609073OpenAlexW3106011230MaRDI QIDQ3442284

Daisuke Yamada

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609073

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Exactly solvable models; Bethe ansatz (82B23)

Related Items (6)

Uniform description of the rigged configuration bijection ⋮ A crystal to rigged configuration bijection and the filling map for type \(D_4^{(3)}\) ⋮ A uniform approach to soliton cellular automata using rigged configurations ⋮ Soliton cellular automaton associated with $D_n^{(1)}$Dn(1)-crystal B2,s ⋮ Rigged configuration bijection and proof of the \(X = M\) conjecture for nonexceptional affine types ⋮ Soliton cellular automaton associated with $G_2^{(1)}$G2(1) crystal base

Cites Work

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• On crystal bases of the \(q\)-analogue of universal enveloping algebras
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• Perfect crystals of \(U_q(G_2^{(1)})\)
• Crystal bases and tensor product decompositions of \(U_ q(G_ 2)\)- modules
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Combinatorial \(R\) matrices for a family of crystals: \(B_n^{(1)}\), \(D_n^{(1)}\), \(A_{2n}^{(2)}\) and \(D_{n+1}^{(2)}\) cases
• The AM(1) automata related to crystals of symmetric tensors
• AFFINE CRYSTALS AND VERTEX MODELS
• Box ball system associated with antisymmetric tensor crystals
• Proof of solitonical nature of box and ball systems by means of inverse ultra-discretization
• Soliton cellular automata associated with crystal bases

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