非对称孪生表示：传递矩阵对称性
Asymmetric Twin Representation: the Transfer Matrix Symmetry
摘要：
描述非对称孪生模型的哈密顿量的对称性在早期的工作中进行了部分研究，我们的目的是推广这些结果的开放的传输矩阵。本着这种精神，我们首先证明，所谓的边界量子代数提供了一个对称性的任何通用的-独立的选择模型-开放的传输矩阵与平凡的左边界。此外还证明了边界量子代数是$B$型Hecke代数的中心化子.然后，我们专注于边界Temperley-Lieb代数的非对称孪生表示。更准确地说，通过利用反射方程所决定的交换关系，我们表明，平凡的边界条件下的传输矩阵享有公认的${\cal U}_{q}(sl_2) \otimes {\cal U}_{\mathrm i}(sl_2)$对称性。当实现非对角边界时，如预期的对称性降低，然而某些熟悉的边界非局部电荷再次与相应的转移矩阵交换。
英文摘要：
The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix. In this spirit we first prove, that the so called boundary quantum algebra provides a symmetry for any generic -- independent of the choice of model -- open transfer matrix with a trivial left boundary. In addition it is shown that the boundary quantum algebra is the centralizer of the $B$ type Hecke algebra. We then focus on the asymmetric twin representation of the boundary Temperley-Lieb algebra. More precisely, by exploiting exchange relations dictated by the reflection equation we show that the transfer matrix with trivial boundary conditions enjoys the recognized ${\cal U}_{q}(sl_2) \otimes {\cal U}_{\mathrm i}(sl_2)$ symmetry. When a non-diagonal boundary is implemented the symmetry as expected is reduced, however again certain familiar boundary non-local charges turn out to commute with the corresponding transfer matrix.
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