Symmetries of spin systems and Birman–Wenzl–Murakami algebra

2009/10/31 by P. P. Kulish, N. Manojlovic, N. Manojlović +1
Mathematics · Physics and Astronomy · #Affine transformation #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Homogeneous space #Integrable system #Multiplet #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum affine algebra #Space (punctuation) #Spin (aerodynamics) #Symmetry (geometry) #hep-th #math.QA #nlin.SI

paper · pdf · doi:10.1063/1.3366259

published as Journal of Mathematical Physics Vol.51, 043516 (2010) · 22 pages; typos corrected

arxiv created 2010/03/02 · openalex publication_date 2010/04/01 · arxiv updated 2010/05/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider integrable open spin chains related to the quantum affine algebras Uq(o(3)ˆ) and Uq(A2(2)). We discuss the symmetry algebras of these chains with the local C3 space related to the Birman–Wenzl–Murakami algebra. The symmetry algebra and the Birman–Wenzl–Murakami algebra centralize each other in the representation space H=⊗1NC3 of the system, and this determines the structure of the spin system spectra. Consequently, the corresponding multiplet structure of the energy spectra is obtained.

Citations

• General boundary conditions for the and open spin chains
• The inverse scattering method approach to the quantum Shabat-Mikhailov model
• Algebraic Bethe ansatz for the Zamolodchikov–Fateev and Izergin–Korepin models with open boundary conditions
• Boundary conditions for integrable quantum systems