Multiple actions of the monodromy matrix elements onto off-shell Bethe vectors in the ##IMG## [http://ej.iop.org/images/1742-5468/2020/9/093104/jstatabacb2ieqn4.gif] {$\mathfrak{g}\mathfrak{l}\left(m\vert n\right)$} -invariant quantum integrable models are calculated. These actions are used to describe recursions for the highest coefficients in the sum formula for the scalar product. For simplicity, detailed proofs are given for the ##IMG## [http://ej.iop.org/images/1742-5468/2020/9/093104/jstatabacb2ieqn5.gif] {$\mathfrak{g}\mathfrak{l}\left(m\right)$} case. The results for the supersymmetric case can be obtained similarly and are formulated without proofs.

中文翻译：

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单峰矩阵元素对## IMG ##的作用[http://ej.iop.org/images/1742-5468/2020/9/093104/toc_jstatabacb2ieqn1.gif] {$ \ mathfrak {g} \ mathfrak {l } \ left（m \ vert n \ right）$}-不变贝特向量

单调矩阵元素在## IMG ## [http://ej.iop.org/images/1742-5468/2020/9/093104/jstatabacb2ieqn4.gif] {$ \ mathfrak {g} \ mathfrak {l} \ left（m \ vert n \ right）$}-计算不变的量子可积模型。这些操作用于描述标量积和公式中最高系数的递归。为简单起见，给出了## IMG ##的详细证明[http://ej.iop.org/images/1742-5468/2020/9/093104/jstatabacb2ieqn5.gif] {$ \ mathfrak {g} \ mathfrak {l} \ left（m \ right）$}大小写。对于超对称情况的结果可以类似地获得，并且在没有证据的情况下被提出。