论文标题
与D型Yangian相关的振荡器实现：朝向正交旋转链的操作Q系统
Oscillator realisations associated to the D-type Yangian: Towards the operatorial Q-system of orthogonal spin chains
论文作者
论文摘要
我们介绍了一个新颖的Lax运营商家族，与Yangian的RTT真实性表示相对应，与$ d $ type Lie代数相关。这些LAX运算符是振荡器类型的，即操作员的一个空间是无限维度的，而另一个是$ \ Mathfrak {so}（2r）$的第一个基本表示。我们使用$ d_3 $的第一个基本表示与$ a_3 $的$ \ mathbf {6} $之间的同构，为此，退化的振荡器型lax矩阵已知，以$ r = 3 $的价格得出lax oterators $ rax运算符。结果用于将LAX矩阵概括为与与$ d_r $的简单连接dynkin图的极端节点相对应的表示的任意等级。每个极端节点处的独立解决方案的多样性由基本表示的维度给出。我们在这些溶液中进一步得出了某些分解公式，并从引入的退化洛杉矶国际矩阵中使用辅助空间中的振荡器构建转移矩阵。最后，我们提供了一些证据表明，构建的转移矩阵是$ \ mathfrak {so}（2r）$ spin链的baxter Q-operators，通过在低长度下以$ d_4 $验证某些QQ - 链条。
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 $\mathfrak{so}(2r)$. We use the isomorphism between the first fundamental representation of $D_3$ and the $\mathbf{6}$ 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 $\mathfrak{so}(2r)$ spin chains by verifying certain QQ-relations for $D_4$ at low lengths.
