Oscillator realisations associated to the D-type Yangian: Towards the operatorial Q-system of orthogonal spin chains
Oscillator realisations associated to the D-type Yangian: Towards the operatorial Q-system of orthogonal spin chains
复制标题
DOI：
10.1016/j.nuclphysb.2020.115063
复制
发表时间：
2020-07-01
影响因子：
2.8
通讯作者：
Frassek, Rouven
中科院分区：
文献类型：
--
作者：
Frassek, Rouven
我们提出了一族新的拉克斯（Lax）算子，它们对应于与D型李代数相关的杨式（Yangian）的RTT实现的表示。这些拉克斯算子是振子型的，即算子的一个空间是无穷维的，而另一个处于so(2r)的第一基本表示中。我们利用D - 3的第一基本表示与A(3)的6之间的同构（对于这种情况，退化振子型拉克斯矩阵是已知的）来推导r = 3时的拉克斯算子。这些结果被用于将拉克斯矩阵推广到任意秩，用于对应于D - r的单链 Dynkin图的极端节点的表示。每个极端节点处独立解的重数由基本表示的维数给出。我们进一步推导了这些解之间的某些分解公式，并从引入的退化拉克斯矩阵构建了辅助空间中有振子的转移矩阵。最后，我们通过验证D - 4在低长度下的某些QQ关系，提供了一些证据表明所构建的转移矩阵是so(2r)自旋链的巴克斯特（Baxter）Q - 算子。（C）2020作者。由爱思唯尔（Elsevier）B.V.出版。
We present a family of novel Lax operators corresponding to representations of the RTT-realisation of the Yangian associated with D-type Lie algebras. These Lax operators are of oscillator type, i.e. one space of the operators is infinite-dimensional while the other is in the first fundamental representation of so (2r). We use the isomorphism between the first fundamental representation of D-3 and the 6 of A(3), for which the degenerate oscillator type Lax matrices are known, to derive the Lax operators for r = 3. The results are used to generalise the Lax matrices to arbitrary rank for representations corresponding to the extremal nodes of the simply laced Dynkin diagram of D-r. The multiplicity of independent solutions at each extremal node is given by the dimension of the fundamental representation. We further derive certain factorisation formulas among these solutions and build transfer matrices with oscillators in the auxiliary space from the introduced degenerate Lax matrices. Finally, we provide some evidence that the constructed transfer matrices are Baxter Q-operators for so(2r) spin chains by verifying certain QQ-relations for D-4 at low lengths. (C) 2020 The Author(s). Published by Elsevier B.V.