论文标题
设置理论杨巴克斯特和反射方程和量子组对称性
Set theoretic Yang-Baxter & reflection equations and quantum group symmetries
论文作者
论文摘要
研究了设定理论的杨巴克斯特与反射方程与量子整合系统之间的连接。我们表明，设定理论$ r $ $ - 标准表示为已知解决方案的曲折。然后，我们专注于反射和扭曲的代数，并得出相关的定义代数关系，以$ r $ $ - matrices作为$ a $ a $ a type hecke hecke algebra $ {\ cal h} _n（q = 1）的解决方案。在反射代数的情况下，我们表明存在``边界''有限的子代数，以选择$ b $ b $ type hecke hecke algebra $ {\ cal b} _n（q = 1，q）$的特殊选择。我们还表明，关键的主张是，相关的双行传输矩阵基本上是根据$ b $ type hecke代数的元素表示的。这是这项调查的基本结果之一，以及边界有限的亚词汇和$ b $ type Hecke代数之间的二元性证明。这些是普遍的陈述，在很大程度上概括了以前的相关发现，并且还允许研究双行传输矩阵的对称性。
Connections between set-theoretic Yang-Baxter and reflection equations and quantum integrable systems are investigated. We show that set-theoretic $R$-matrices are expressed as twists of known solutions. We then focus on reflection and twisted algebras and we derive the associated defining algebra relations for $R$-matrices being Baxterized solutions of the $A$-type Hecke algebra ${\cal H}_N(q=1)$. We show in the case of the reflection algebra that there exists a ``boundary'' finite sub-algebra for some special choice of ``boundary'' elements of the $B$-type Hecke algebra ${\cal B}_N(q=1, Q)$. We also show the key proposition that the associated double row transfer matrix is essentially expressed in terms of the elements of the $B$-type Hecke algebra. This is one of the fundamental results of this investigation together with the proof of the duality between the boundary finite subalgebra and the $B$-type Hecke algebra. These are universal statements that largely generalize previous relevant findings, and also allow the investigation of the symmetries of the double row transfer matrix.
