Study of integrable structure inquanteem integrable model

Quanteem可积模型中的可积结构研究

• 批准号: 10640016
• 负责人: NAKANISHI Tomoki
• 金额: $ 2.05万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640016/
• 关键词: Bethe ansatz; Heisenberg model; quantum group; intergrable models; ベーテ方程式; ベーテ仮説; Bethe方程式; 可積分格子模型

We obtain the following new results on the integrable structure of integrable lattice models.1. The formal completeness theorem on the Bethe equation for the XXZ-type spin models. (Nakanishi, Kuniba, Tsuboi (Tokyo Univ.))By classifying the string solutions of the Bethe equation for the XXZ-type spin models in the q=0 limit, we showed that, under the Kirillov-Reshetikhin (KR) conjecture on the KR modules of the quantum affine algebras, the power series formula of the character of the KR module representing the formal completeness of the XXZ-type spin models holds for any affine Lie algebra.2. Reformulation of the Kirillov-Reshetikhin conjecture by the canonical solutions of the Q-systems. (Nakanishi, Kuniba, Tsuboi (Tokyo Univ.))By observing the principle mechanism for various formulae and theorems obtained in the study of 1, we completely clarified the relation between these power series formulae representing the formal completeness and the underlying functional (algebraic) equations (Q-system of KR-type). Namely, we introduce a kind of functional equations (finite Q-system) for a finite number of functions of a finite number of variables. A finite Q-system has a remarkable property that its unique solution admits two power series formula by the Lagrange inversion formula for several variables. They are exactly a finite-variable analogue of the formal completeness formulae for the XXX-type and XXZ-type models. The formal completeness formula can be obtained as the projective limit of this formula.

我们在可集成晶格模型的可集成结构上获得以下新结果。1。 XXZ型自旋模型的BETHE方程式上的形式完整定理。 (Nakanishi, Kuniba, Tsuboi (Tokyo Univ.))By classifying the string solutions of the Bethe equation for the XXZ-type spin models in the q=0 limit, we showed that, under the Kirillov-Reshetikhin (KR) conjecture on the KR modules of the quantum affine algebras, the power series formula of the character of the KR module representing the formal completeness XXZ型旋转模型的任何仿射模型都有代数。2。 Q-Systems的规范解决方案对Kirillov-Reshetikhin的重新重新制定。 （Nakanishi，Kuniba，Tsuboi（Tokyo Univ。））通过观察1在研究中获得的各种公式和定理的主要机制，我们完全阐明了代表正式完整性的这些功率序列公式之间的关系（Q-Sype）。也就是说，我们为有限数量的变量的有限函数引入了一种函数方程（有限Q-System）。有限的Q系统具有非凡的属性，其独特的解决方案通过Lagrange反演公式为多个变量提供了两个功率系列公式。它们正是XXX型和XXZ型模型的形式完整公式的有限变量类似物。正式的完整公式可以作为此公式的投影限制。

项目成果

T.Nakanishi, (A.Kuniba, Z.Tsuboi): "The Bethe equation at q=0, the Mobius inversion formula, and areight Multiplicities : III The Xn^r case"Letters in Mathematical Physics. 印刷中.

T. Nakanishi，（A.Kuniba，Z.Tsuboi）：“q=0 时的贝特方程、莫比乌斯反演公式和正重数：III Xn^r 情况”数学物理学快报正在出版。

T.Nakanishi(with A.Kuniba, Z.Ysuboi): "The Bethe equation at q=0, the Mobius inversion formula, and weight multiplicities : III THE X_n case"Letters in Mathematical Physics. (in press).

T.Nakanishi（与 A.Kuniba、Z.Ysuboi）：“q=0 时的贝特方程、莫比乌斯反演公式和权重重数：III X_n 情况”数学物理学快报。

T.Nakanishi, A.Kuniba, Z.Tsuboi: "The Bethe equation at q=0, the Mobius inversion formula, and weight multiplicities : III The X^<(r)>_n case"Letters in Mathematical Physics. (印刷中).

T.Nakanishi、A.Kuniba、Z.Tsuboi：“q=0 时的贝特方程、莫比乌斯反演公式和权重重数：III X^<(r)>_n 情况”《数学物理学快报》（正在出版）。 ）。

T.Nakanishi, (A.Kuniba, Z.Tsuboi): "The canonical sdutions of the Q-systems and the Kirillov-Reshetikhin conjecture"Communications in Mathematical Physics. 印刷中.

T. Nakanishi，（A.Kuniba，Z.Tsuboi）：“Q 系统和基里洛夫-列谢蒂欣猜想的规范研究”数学物理通讯出版。

A.Kuniba,T.Nakanishi: "The Bethe equation at 9=0,the Mobius inversion formula, and weight multiplicities II, Xn case "J.Algebra. (掲載予定).

A.Kuniba、T.Nakanishi：“9=0​​ 时的 Bethe 方程、莫比乌斯反演公式和权重多重性 II，Xn 情况”J.Algebra。