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一次元量子可積分系と付随する直交多項式の理論と応用

一维量子可积系统及相关正交多项式的理论与应用

基本信息

批准号：
12740250
负责人：
宇治野秀晃
金额：
$ 1.02万
依托单位：
Gunma National College of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Encouragement of Young Scientists (A)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

项目摘要

交付申請書に記載した研究の目的および本年度の研究実施計画に基づき,本年度は,非対称多変数直交多項式を固有関数の直交関数系に持つ,Calogero-Sutherlandタイプの量子可積分系に関する研究を進めた。trigonometricタイプのSutherland模型,Ruijsenaars模型の固有関数については,それぞれリー代数,アファイン・リー代数のルート系に関連させて,一般化できることが知られている。また対応する非対称直交多項式固有関数もルート系に付随するヘッケ代数,アファイン・ヘッケ代数を用いて統一的に扱うことが可能であることが,CherednikやOpdamらによって明らかにされていた。同様の定式化が与えられていなかった,調和振動子型の外場を持つCalogeroタイプの模型の固有関数に対応する,多変数エルミート多項式,多変数ラゲール多項式について,それぞれA型,B型のルート系に関連させた形式での代数的な定式化を与えた。Jacobi多項式やMacdonald-Koornwinder多項式の場合とほぼパラレルな定式化で解析を行い,非対称多変数エルミート多項式と非対称多変数ラゲール多項式の代数的な構成法と,ノルムの計算,対称化・反対称化に成功した。

The purpose of this year's study is to carry out a basic plan for this year's research. This year, non-symmetric multiplicity orthogonal multinomial formula inherent number orthogonal numerical system is maintained, and the research of Calogero-Sutherland quantum sub-system is in progress. Sutherland model, trigonometric model, Ruijsenaars model, algebra, algebra and algebra. This is not known as the inherent number of orthogonal polynomials, which is related to the algebra of orthogonal polynomials. the algebra of orthogonal polynomials is related to the algebra of orthogonal polynomials. the algebra of orthogonal polynomials is related to the number of orthonormal polynomials, while the algebra of orthogonal polynomials is related to the algebra of orthogonal polynomials. the algebra of orthogonal polynomials is based on the number of orthogonal polynomials, which is related to the number of orthogonal polynomials, which is not the inherent number of orthogonal polynomials. The number of orthogonal polynomials is related to the number of orthogonal polynomials, which is related to the algebra of orthogonal polynomials. the algebra of orthogonal polynomials is related to the algebra of orthogonal polynomials. the algebra of orthogonal polynomials is related to the algebra of orthogonal polynomials. In the same way, the stereotype and the vibrator type of the field hold the inherent number of the Calogero model, the number of the model, the number of the polynomial, the number of the multinomial, the type A, the type B and the form of the algebra. Jacobi Polynomials "Macdonald-Koornwinder Polynomials", "compound Polynomials", "customization" parsing rows, "non-symmetric Polymers", "non-symmetric Polynomials"non-symmetric Polynomials", "formation method" of Polynomials Algebra, "calculation", "inverse scaling", "success".