论文标题
四面体方程与量化的六个vertex模型相关的新解决方案
New solutions to the tetrahedron equation associated with quantized six-vertex models
论文作者
论文摘要
我们为$ rlll = lllr $的四面体方程提供了一个新解决方案，其中$ l $运算符被视为量化的六个vertex型号，其玻尔兹曼的权重是$ q $ osciLLTATOR或$ q $ $ q $ -weyl algebras的特定表示。当三$ l $与$ q $ - 苏联代数相关联时，$ r $与已知的量化坐标环$ a_q（sl_3）$相吻合。另一方面，基于$ q $ -weyl代数的$ l $ s导致了新的$ r $ $，其元素要么被分解或表示为终止$ q $ Q $ - hyphepertric类型系列。
We present a family of new solutions to the tetrahedron equation of the form $RLLL=LLLR$, where $L$ operator may be regarded as a quantized six-vertex model whose Boltzmann weights are specific representations of the $q$-oscillator or $q$-Weyl algebras. When the three $L$'s are associated with the $q$-oscillator algebra, $R$ coincides with the known intertwiner of the quantized coordinate ring $A_q(sl_3)$. On the other hand, $L$'s based on the $q$-Weyl algebra lead to new $R$'s whose elements are either factorized or expressed as a terminating $q$-hypergeometric type series.
