标题： 反射算子与超几何 II: $SL(2, \mathbb{C})$ 自旋链 显示英文标题

标题： Reflection operator and hypergeometry II: $SL(2, \mathbb{C})$ spin chain

摘要： 我们研究了非紧开链$SL(2, \mathbb{C})$自旋链，并构造了单站点链中转移矩阵的$B$元素的本征函数。 此构造中出现的反射算符可用于用$n-1$站点的本征函数表示$n$站点的本征函数，这一一般性结果简要宣布。 我们证明了一站点情况下的构造本征函数的正交性和完备性，将其表达为复数域上的超几何函数，并推导出具有通用$SL(2,\mathbb{C})$不变量的$\mathbb{R}$算符的反射算符方程。 显示英文摘要

摘要： We consider noncompact open $SL(2, \mathbb{C})$ spin chain and construct eigenfunctions of $B$-element of monodromy matrix for the simplest case of the chain with one site. The reflection operator appearing in this construction can be used to express eigenfunction for $n$ sites in terms of the eigenfunction for $n-1$ sites, this general result is briefly announced. We prove orthogonality and completeness of constructed eigenfunctions in the case of one site, express them in terms of the hypergeometric function of the complex field and derive the equation for the reflection operator with the general $SL(2,\mathbb{C})$-invariant $\mathbb{R}$-operator.