Symmetries of spin systems and Birman-Wenzl-Murakami algebra

Details Symmetries of spin systems and Birman-Wenzl-Murakami algebra Symmetries of spin systems and Birman-Wenzl-Murakami algebra

2009-10-21

arxiv.org/abs/0910.4036v3

Journal of Mathematical Physics Vol.51, 043516 (2010)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages; typos corrected

Scientific paper

10.1063/1.3366259

We consider integrable open spin chains related to the quantum affine algebras U_q(o(3)) and U_q(A_2^{(2)}). We discuss the symmetry algebras of these chains with the local C^3 space related to the Birman-Wenzl-Murakami algebra. The symmetry algebra and the Birman-Wenzl-Murakami algebra centralize each other in the representation space, and this defines the structure of the spin system spectra. Consequently, the corresponding multiplet structure of the energy spectra is obtained.

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