Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators

FRT presentation of the Onsager algebras

A presentation à la Faddeev-Reshetikhin-Takhtajan (FRT) of the Onsager, augmented Onsager and sl(2)-invariant Onsager algebras is given, using the framework of the non-standard classical Yang-Baxter algebras. Associated current algebras are identified, and generating functions of mutually commuting quantities are obtained.

FRT presentation of classical Askey-Wilson algebras

Automorphisms of the infinite dimensional Onsager algebra are introduced. Certain quotients of the Onsager algebra are formulated using a polynomial in these automorphisms. In the simplest case, the quotient coincides with the classical analog of the Askey-Wilson algebra. In the general case, generalizations of the classical Askey-Wilson algebra are obtained. The corresponding class of solutions of the non-standard classical Yang-Baxter algebra are constructed, from which a generating function of elements in the commutative subalgebra is derived. We provide also another presentation of the Ons…

gl_n Yangian中的组合扭

Combinatorial twists in gl_n Yangians

本文引入特殊集合论杨-巴克斯特代数并分析其霍普夫代数结构与泛R矩阵，将Drinfel'd扭应用于增广gl_n Yangian，得到其扭转变换版本。

Onsager方法中的半无限XXZ链

The half-infinite XXZ chain in Onsager's approach

在最近发展的Onsager方法中考虑了具有一般可积边界条件的半无限XXZ开自旋链。受有限大小的情况下，对于任何类型的可积边界条件，它示出的传递矩阵是简单地表示在最近推出的一种新类型的电流代数的元素。在大规模制度$-1<q<0$，水平一无限维表示（$q-$顶点运营商）的新的电流代数的构造，以对角化的传输矩阵。对于对角边界条件，本文推广了Jimbo { \it et al.}都被找到了对于上（或下）非对角边界条件，提出了一种解法。使用$q-$玻色子在当前代数的表示理论中制定真空和激发态，为计算非对角边界的关联函数的积分表示开辟了道路。最后，$q$通用的隐藏的非阿贝尔对称性的哈密顿量的长期存在的问题得到解决：它是与$q-$ Onsager代数（通用非对角的情况下）或增广的$q-$ Onsager代数（通用对角的情况下）。

On diagonal solutions of the reflection equation

We study solutions of the reflection equation associated with the quantum affine algebra $U_{q}(\hat{gl}(N))$ and obtain diagonal K-operators in terms of the Cartan elements of a quotient of $U_{q}(gl(N))$. We also consider intertwining relations for these K-operators and find an augmented q-Onsager algebra like symmetry behind them.

反射方程的中心推广和Miki公式的一个类似

Central extension of the reflection equations and an analog of Miki's formula

引入了两种不同类型的中心扩张量子反射代数。实现的杨-巴克斯特代数的中心扩展的元素方面展出。确定了共同作用图。对于特殊情况下的$U_q(\hat{sl_2})$，实现的元素满足Zamolodchikov-Faddeev代数-一个“边界”模拟三木的公式-也提出了，提供一个自由场实现的$O_q(\hat{sl_2})$（q-Onsager）电流。