标题： 非紧致的SL(2,R)自旋链 显示英文标题

标题： Noncompact SL(2,R) spin chain

摘要： 我们研究可积自旋链模型——非紧致的SL(2,R)自旋磁体。 自旋算符被实现为SL(2,R)群的主系列表示的生成元。 以显式形式，我们构造了R-矩阵、Baxter Q-算符以及过渡核到分离变量(SoV)表示。 通过Baxter Q-算符，推导出本征态能量和准动量的表达式。 建立了Baxter算符本征值作为谱参数函数的解析性质。 应用图示方法，我们计算了Sklyanin的分离变量积分测度，并得到了模型谱问题解的Q-算符本征值表示。 我们证明，向SoV表示的过渡核分解为某些算符的乘积，每个算符仅依赖于单一分离变量。 显示英文摘要

摘要： We consider the integrable spin chain model - the noncompact SL(2,R) spin magnet. The spin operators are realized as the generators of the unitary principal series representation of the SL(2,R) group. In an explicit form, we construct R-matrix, the Baxter Q-operator and the transition kernel to the representation of the Separated Variables (SoV). The expressions for the energy and quasimomentum of the eigenstates in terms of the Baxter Q-operator are derived. The analytic properties of the eigenvalues of the Baxter operator as a function of the spectral parameter are established. Applying the diagrammatic approach, we calculate Sklyanin's integration measure in the separated variables and obtain the solution to the spectral problem for the model in terms of the eigenvalues of the Q-operator. We show that the transition kernel to the SoV representation is factorized into a product of certain operators each depending on a single separated variable.