Representation theoretical aproach to multi-variate elliptic hypergeometric functions

多元椭圆超几何函数的表示理论方法

• 批准号: 22540022
• 负责人: KONNO Hitoshi
• 金额: $ 2.75万
• 依托单位: Hiroshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540022/
• 关键词: 楕円量子群; 楕円超幾何関数; アフィン リー環; 楕円関数; 量子群; 超幾何関数; Sklyanin代数; 可解格子模型; Z-代数; W-代数; アフィンリー環

We have reformulated the two elliptic algebras U_{q,p}(g) and E_{q,p}(g) as topological algebras over the ring of formal power series in p and shown that they are isomorphic for g=gl_n. We also have formulated the dynamical quantum Z-algebras associated with U_{q,p}(g), and shown that the irreducibility of the U_{q,p}(g)-modules is governed by the corresponding Z-modules. As for the multivariate elliptic hypergeometric functions, we have shown that the sl_n type found by Kajihara-Noumi and Rosengren is given by a certain tensor product of the symmetric fusions of the sl_n type vertex-face intertwining vectors and their duals. Furthermore, as an application of the representations of U_{q,p}(sl_2), we have derived and analyzed the structure factor of the massless XXZ model exactly.

本文将两个椭圆代数U_{q，p}（g）和E_{q，p}（g）转化为p中形式幂级数环上的拓扑代数，并证明了它们对g=gl_n是同构的。我们还建立了与U_{q，p}（g）相关的动力量子Z-代数，并证明了U_{q，p}（g）-模的不可约性由相应的Z-模决定。对于多元椭圆超几何函数，我们证明了由Kajihara-Noumi和Rosengren发现的sl_n型是由sl_n型顶点-面交织向量的对称融合与它们的乘积的某个张量积给出的。作为U_{q，p}（sl_2）表示的应用，我们还精确地导出和分析了无质量XXZ模型的结构因子。

项目成果

XXZ模型零質量相の2スピノン形状因子

XXZ模型零质量相的2-自旋形状因子

• 发表时间: 2011
• 作者: J-S Caux;H. Konno;M.Sorrell;R.Weston
• 通讯作者: R.Weston

Elliptic Quantum Group U_q,_p(ĝ) and Deformed W -Algebras

椭圆量子群 U_q,_p(ĝ) 和变形 W 代数

• 发表时间: 2013
• 作者: R.M.Farghly;H. Konno and K.Oshima;H. Konno and K.Oshima;H. Konno;H. Konno;H. Konno and K.Oshima;H. Konno
• 通讯作者: H. Konno

XXZ模型の零質量相における2スピノン形状因子と構造因子

XXZ模型零质量相的2-自旋形状因子和结构因子

• 发表时间: 2011
• 作者: J-S Caux;H. Konno;M.Sorrell;R.Weston
• 通讯作者: R.Weston

Elliptic Quan- tum Algebra U_q,p(B^<(1)> _N ) and Vertex Oper- ators

椭圆量子代数 U_q,p(B^<(1)> _N ) 和顶点算子

• 期刊: 研究会"第16回代数群と量子群の表現論"報告集
• 作者: R.M.Farghly;H. Konno and K.Oshima;H. Konno and K.Oshima
• 通讯作者: H. Konno and K.Oshima

Elliptic Quantum Groups, Quantum Z-Algebras and Deformed W - Algebras

椭圆量子群、量子 Z 代数和变形 W 代数

• 发表时间: 2013
• 作者: R.M.Farghly;H. Konno and K.Oshima;H. Konno and K.Oshima;H. Konno
• 通讯作者: H. Konno