Representations of double affine Hecke algebras and their applications to integrable systems

双仿射 Hecke 代数的表示及其在可积系统中的应用

• 批准号: 21740005
• 负责人: KASATANI Masahiro
• 金额: $ 1.25万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740005/
• 关键词: アフィンヘッケ環; qKZ方程式; Macdonald多項式; Koornwinder多項式

(1) We formulated boundary qKZ equation in terms of the polynomial representation of the double affine Hecke algebra (DAHA) of type C^∨C. We gave a procedure to construct its polynomial solutions from solutions for an eigenvalue problem. Some special solutions are constructed by non-symmetric Koornwinder polynomials. (2) We confirmed that it will be possible to formulate a construction of polynomial solutions for a degenerate limit of the qKZ equation (with no boundary) in terms of the polynomial representation of degenerate DAHA. (3) We suggest an equality between non-symmetric Macdonald polynomials at roots of unity and Schur symmetric polynomials.

（1）我们根据C^∨c型的双仿射Hecke代数（DAHA）的多项式表示，制定了边界QKZ方程。我们给出了一种从解决特征值问题的解决方案中构建其​​多项式溶液的程序。一些特殊的解决方案是由非对称的Koornwinder多项式构建的。 （2）我们确认，可以根据QKZ方程的退化极限（无边界）制定多项式溶液的构造，以简化DAHA的多项式表示。 （3）我们建议在Unity和Schur对称多项式的根部的非对称MacDonald多项式之间平等。

项目成果

Boundary Quantum Knizhnik-Zamolodchikov Equation

边界量子 Knizhnik-Zamolodchikov 方程

• 发表时间: 2010
• 期刊: New Trends in Quantum Integrable Systems : Proceedings of the Infinite Analysis 09
• 作者: Masanori Asakura;Kanetomo Sato;Masanori Asakura;Masanori Asakura;朝倉政典;朝倉政典;朝倉政典;M.Asakura;朝倉政典;朝倉政典;朝倉政典;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;大坪紀之;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;大坪紀之;Masahiro Kasatani
• 通讯作者: Masahiro Kasatani

境界付きqKZ方程式と非対称Koornwinder多項式について

关于有界 qKZ 方程和非对称 Koornwinder 多项式

• 发表时间: 2010
• 作者: Masanori Asakura;Kanetomo Sato;Masanori Asakura;Masanori Asakura;朝倉政典;朝倉政典;朝倉政典;M.Asakura;朝倉政典;朝倉政典;朝倉政典;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;大坪紀之;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;大坪紀之;Masahiro Kasatani;笠谷昌弘;笠谷昌弘;笠谷昌弘
• 通讯作者: 笠谷昌弘

The qKZ equation and its polynomial solutions

qKZ方程及其多项式解

• 发表时间: 2010
• 作者: Masanori Asakura;Kanetomo Sato;Masanori Asakura;Masanori Asakura;朝倉政典;朝倉政典;朝倉政典;M.Asakura;朝倉政典;朝倉政典;朝倉政典;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;大坪紀之;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;大坪紀之;Masahiro Kasatani;笠谷昌弘;笠谷昌弘;笠谷昌弘;Masahiro Kasatani
• 通讯作者: Masahiro Kasatani

$C^/vee C$型DAHAの多項式表現と境界付きqKZ方程式について

$C^/vee 关于C$型DAHA和有界qKZ方程的多项式表示

• 发表时间: 2010
• 作者: Masanori Asakura;Kanetomo Sato;Masanori Asakura;Masanori Asakura;朝倉政典;朝倉政典;朝倉政典;M.Asakura;朝倉政典;朝倉政典;朝倉政典;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;大坪紀之;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;大坪紀之;Masahiro Kasatani;笠谷昌弘;笠谷昌弘
• 通讯作者: 笠谷昌弘

C∨C型DAHAの多項式表現と境界付きqKZ方程式について

关于C∨C型DAHA和有界qKZ方程的多项式表示

• 发表时间: 2010
• 作者: Masanori Asakura;Kanetomo Sato;Masanori Asakura;Masanori Asakura;朝倉政典;朝倉政典;朝倉政典;M.Asakura;朝倉政典;朝倉政典;朝倉政典;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;大坪紀之;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;Noriyuki Otsubo;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;Noriyuki Otsubo;大坪紀之;大坪紀之;大坪紀之;Masahiro Kasatani;笠谷昌弘
• 通讯作者: 笠谷昌弘