Symmetries of spin systems and Birman-Wenzl-Murakami algebra

TL;DR

This paper explores the symmetry structures of integrable open spin chains linked to specific quantum affine algebras, revealing how the Birman-Wenzl-Murakami algebra governs the spectral multiplet structure.

Contribution

It establishes the mutual centralization of the symmetry algebra and the Birman-Wenzl-Murakami algebra in the representation space of these spin chains, elucidating their spectral properties.

Findings

Symmetry algebra and Birman-Wenzl-Murakami algebra centralize each other.

The spectral multiplet structure is derived from this algebraic relationship.

The work connects algebraic symmetries to physical spectra in spin systems.

Abstract

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.