### Abstract

Using anisotropic R-matrices associated with affine Lie algebras gˆ (specifically, A_{2n} ^{(2)}, A_{2n−1} ^{(2)}, B_{n} ^{(1)}, C_{n} ^{(1)}, D_{n} ^{(1)}) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of gˆ. We show that these transfer matrices also have a duality symmetry (for the cases C_{n} ^{(1)} and D_{n} ^{(1)}) and additional Z_{2} symmetries that map complex representations to their conjugates (for the cases A_{2n−1} ^{(2)}, B_{n} ^{(1)} and D_{n} ^{(1)}). A key simplification is achieved by working in a certain “unitary” gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.

Original language | English (US) |
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Pages (from-to) | 91-134 |

Number of pages | 44 |

Journal | Nuclear Physics B |

Volume | 930 |

DOIs | |

State | Published - May 2018 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics B*,

*930*, 91-134. https://doi.org/10.1016/j.nuclphysb.2018.02.023