量子群不变量XXZ自旋链厄米特化：关于不变量积的一个猜想
Turning the Quantum Group Invariant XXZ Spin-Chain Hermitian: A Conjecture on the Invariant Product
摘要：
这是以前与罗伯特·韦斯顿在量子群不变XXZ自旋链（math-ph/0703085）上的联合工作的延续。本文简要回顾了这一可积模型的拟厄米性的已有结果，并结合一个新的内积的构造，使Hamilton算子和Temperley-Lieb代数的表示成为厄米性的.该方法是纯代数的，一个开始的定义，一个积极的功能超过Temperley-Lieb代数的值可以计算图形。利用C ~*-代数的GNS构造方法，构造了形变参数q位于单位圆特殊截面上的Temperley-Lieb代数的自伴表示.本文的主要猜想是酉等价的GNS表示与表示在以前的文件采用PT对称性和准厄米性的想法。给出了一个显式的例子。
英文摘要：
This is a continuation of a previous joint work with Robert Weston on the quantum group invariant XXZ spin-chain (math-ph/0703085). The previous results on quasi-Hermiticity of this integrable model are briefly reviewed and then connected with a new construction of an inner product with respect to which the Hamiltonian and the representation of the Temperley-Lieb algebra become Hermitian. The approach is purely algebraic, one starts with the definition of a positive functional over the Temperley-Lieb algebra whose values can be computed graphically. Employing the Gel'fand-Naimark-Segal (GNS) construction for C*-algebras a self-adjoint representation of the Temperley-Lieb algebra is constructed when the deformation parameter q lies in a special section of the unit circle. The main conjecture of the paper is the unitary equivalence of this GNS representation with the representation obtained in the previous paper employing the ideas of PT-symmetry and quasi-Hermiticity. An explicit example is presented.
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