AI 中文总结
研究有理非齐次gl(M)自旋链，通过在辅助福克空间实现gl(M)定义主T算子，关联巴克斯特Q算子的两种构造，给出Q算子显式留数公式及L算子相关收缩结果。
AI 中文摘要
主T算子是转移矩阵的生成函数和修正KP（mKP）层次结构的τ函数。传统上它通过舒尔函数展开引入，其系数是满足切列德尼克 - 巴扎诺夫 - 雷谢蒂金行列式公式的融合转移矩阵。对于有理非齐次gl(M)自旋链，我们给出了一个替代定义：在由有限多个施温格玻色子族生成的辅助福克空间上实现gl(M)，从所得的L算子形成单值矩阵，并将主T算子定义为其在福克空间上的迹。豪对偶性进而重现舒尔函数展开。这种实现关联了巴克斯特Q算子的两种构造。在[arXiv:1112.3310]（另见[arXiv:1010.4022]）的构造中，Q算子从主T算子关于选定三田变量的留数得到。在[arXiv:1010.3699]的构造中，它们用振子形式的退化杨式L算子定义。当选定三田变量接近边界扭转特征值的倒数时，定义迹出现极点。对这个L算子进行适当重标度后，在归一化极限中只有对最高阶极点有贡献的项留存；在取迹之前，它们形成第二种构造的退化杨式L算子。迹然后给出了相应Q算子的显式留数公式。独立地，这个L算子在具有固定总占据数的子空间上的霍尔斯坦 - 普里马科夫型大占据数收缩产生相同的退化杨式L算子。
英文摘要
The master T-operator is a generating function for transfer matrices and a tau-function of the modified KP (mKP) hierarchy. It is conventionally introduced through a Schur-function expansion whose coefficients are fused transfer matrices satisfying the Cherednik--Bazhanov--Reshetikhin determinant formula. For rational inhomogeneous gl(M) spin chains, we give an alternative definition: we realize gl(M) on an auxiliary Fock space generated by finitely many families of Schwinger bosons, form a monodromy matrix from the resulting L-operator, and define the master T-operator as its trace over the Fock space. Howe duality then reproduces the Schur-function expansion. This realization relates two constructions of Baxter Q-operators. In the construction of [arXiv:1112.3310] (see also [arXiv:1010.4022]), the Q-operators are obtained from residues of the master T-operator with respect to selected Miwa variables. In the construction of [arXiv:1010.3699], they are defined using degenerate Yangian L-operators in oscillator form. When selected Miwa variables approach the inverses of boundary-twist eigenvalues, the defining trace develops poles. After a suitable rescaling of this L-operator, only the terms contributing to the highest-order pole survive in the normalized limit; before the trace is taken, they form the degenerate Yangian L-operator of the second construction. The trace then gives an explicit residue formula for the corresponding Q-operator. Independently, a Holstein--Primakoff-type large-occupation-number contraction of this L-operator on subspaces with fixed total occupation numbers yields the same degenerate Yangian L-operator.
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