3-JACK多项式与杨-巴克斯特方程

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2023-02-01 DOI:10.1016/S0034-4877(23)00012-5

Na Wang

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引用次数: 3

摘要

在坐标系O - xyz平面z = n上的三维杨氏图的每个切片都是二维杨氏图。本文给出了二维杨氏图的杰克多项式如何构成三维杨氏图的杰克多项式，称为3-杰克多项式。给出了总箱数小于4的三维杨图的3-Jack多项式的具体表达式，并找到了求每个三维杨图的3-Jack多项式的方法。当三维Young图在z轴方向上只有一层时，3-Jack多项式成为二维Young图的Jack多项式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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3-JACK POLYNOMIALS AND YANG--BAXTER EQUATION

Every slice of a 3D Young diagram on the plane z = n in the coordinate system O - xyz is a 2D Young diagram. In this paper, we show how Jack polynomials of 2D Young diagrams constitute a Jack polynomial of 3D Young diagram, which is called 3-Jack polynomial. We give the specific expressions of 3-Jack polynomials of 3D Young diagrams of total box number less than 4, and we find a method to obtain 3-Jack polynomials for every 3D Young diagram. 3-Jack polynomials become Jack polynomials of 2D Young diagrams when 3D Young diagrams have only one layer in the z-axis direction.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.