标题： 非线性全纯超对称，Dolan-Grady关系和Onsager代数 显示英文标题

标题： Nonlinear holomorphic supersymmetry, Dolan-Grady relations and Onsager algebra

摘要： Recently, it was noticed by us that the nonlinear holomorphic supersymmetry of order $n\in\N, n>1$, (n-HSUSY) has an algebraic origin. We show that the Onsager algebra underlies n-HSUSY and investigate the structure of the former in the context of the latter. A new infinite set of mutually commuting charges is found which, unlike those from the Dolan-Grady set, include the terms quadratic in the Onsager algebra generators. This allows us to find the general form of the superalgebra of n-HSUSY and fix it explicitly for the cases of $n=2,3,4,5,6$. The similar results are obtained for a new, contracted form of the Onsager algebra generated via the contracted Dolan-Grady relations. As an application, the algebraic structure of the known 1D and 2D systems with n-HSUSY is clarified and a generalization of the construction to the case of nonlinear pseudo-supersymmetry is proposed. Such a generalization is discussed in application to some integrable spin models and with its help we obtain a family of quasi-exactly solvable systems appearing in the PT-symmetric quantum mechanics. 显示英文摘要

摘要： Recently, it was noticed by us that the nonlinear holomorphic supersymmetry of order $n\in\N, n>1$, (n-HSUSY) has an algebraic origin. We show that the Onsager algebra underlies n-HSUSY and investigate the structure of the former in the context of the latter. A new infinite set of mutually commuting charges is found which, unlike those from the Dolan-Grady set, include the terms quadratic in the Onsager algebra generators. This allows us to find the general form of the superalgebra of n-HSUSY and fix it explicitly for the cases of $n=2,3,4,5,6$. The similar results are obtained for a new, contracted form of the Onsager algebra generated via the contracted Dolan-Grady relations. As an application, the algebraic structure of the known 1D and 2D systems with n-HSUSY is clarified and a generalization of the construction to the case of nonlinear pseudo-supersymmetry is proposed. Such a generalization is discussed in application to some integrable spin models and with its help we obtain a family of quasi-exactly solvable systems appearing in the PT-symmetric quantum mechanics.