论文标题
量子级超甲虫的Khoroshkin-Tolstoy方法
Khoroshkin-Tolstoy approach for quantum superalgebras
论文作者
论文摘要
量子整合模型研究的量子代数方法的核心对象是通用$ r $ -matrix，它是两个量子代数副本的完整张量产品的元素。通过选择该张量产品因素的表示形式来构建各种可集成性对象。为通用$ r $ -matrix构建明确表达式有两种方法。一个基于量子双重结构，另一个基于$ q $ - 交易者的概念。在量子超级甲虫的情况下，我们不能使用第一种方法，因为我们不知道lusztig自动形态的明确表达。一个人可以使用第二种方法，但是它需要与各向同性根有关的一些修改。在本文中，我们提供了对方法的必要修改，并使用它来找到与量子超级级别$ \ mathrm u_q（\ Mathcal {l}（\ Mathfrak {sl} _ {m | n}）相关的量子集成系统的$ r $ operator。
The central object of the quantum algebraic approach to the study of quantum integrable models is the universal $R$-matrix, which is an element of a completed tensor product of two copies of quantum algebra. Various integrability objects are constructed by choosing representations for the factors of this tensor product. There are two approaches to constructing explicit expressions for the universal $R$-matrix. One is based on the quantum double construction, and the other is based on the concept of the $q$-commutator. In the case of a quantum superalgebra, we cannot use the first approach, since we do not know an explicit expression for the Lusztig automorphisms. One can use the second approach, but it requires some modifications related to the presence of isotropic roots. In this article, we provide the necessary modification of the method and use it to find an $R$-operator for quantum integrable systems related to the quantum superalgebra $\mathrm U_q(\mathcal{L}(\mathfrak{sl}_{M | N}))$.
