New Solutions to the Tetrahedron Equation Associated with Quantized Six-Vertex Models
New Solutions to the Tetrahedron Equation Associated with Quantized Six-Vertex Models
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DOI：
10.1007/s00220-023-04711-y
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发表时间：
2022-08
影响因子：
2.4
通讯作者：
A. Kuniba;Shuichiro Matsuike;Akihito Yoneyama
中科院分区：
文献类型：
--
作者：
A. Kuniba;Shuichiro Matsuike;Akihito Yoneyama
本文给出了形式为的四面体方程的一族新解，其中L算子可以看作是一个量子化的六顶点模型，其玻尔兹曼权是q振子或q-Weyl代数的具体表示.当三个L与q-振子代数相关联时，R与量子化坐标环的已知缠绕子相一致。另一方面，基于q-Weyl代数的L's导致新的R's，其元素要么被分解，要么被表示为终止的q-超几何型级数。
We present a family of new solutions to the tetrahedron equation of the form, whereLoperator may be regarded as a quantized six-vertex model whose Boltzmann weights are specific representations of theq-oscillator orq-Weyl algebras. When the threeL’s are associated with theq-oscillator algebra,Rcoincides with the known intertwiner of the quantized coordinate ring. On the other hand,L’s based on theq-Weyl algebra lead to newR’s whose elements are either factorized or expressed as a terminatingq-hypergeometric type series.