Representation theory of Elliptic Quantum Groups and Deformation of W-algebra
椭圆量子群的表示论与W-代数的变形
基本信息
- 批准号:15540033
- 负责人:
- 金额:$ 2.24万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2003
- 资助国家:日本
- 起止时间:2003 至 2005
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
1.Drinfeld realization of B_<q,λ>(g) : For g=A^<(2)>_2, we realized the L-operator of the elliptic quantum group B_<q,λ>(g) in terms of the currents of the elliptic algebra U_<q,p>(g). Then we showed the isomorphism U_<q,p>(g)=^^〜B_<q,λ>(g)【cross product】 C{H^^^} as an associative algebra. Here C{H^^^} denotes some Heisenberg algebra. Futhermore, we constructed the level-1 free field representation of U_<q,p> (A^<(2)>_2), and showed that the vertex operators of U_<q,p>(A^<(2)>_2) provide a realization of the lattice vertex operators of A^<(2)>_2 SOS model in the algebraic analysis formulation.2.B_<q,λ>(sl^^^_n) and the deformed W_n-algebra : Extending the results in the cases g=A^<(1)>_1,A^<(2)>_2 we showed that a fusion of a pair of the level-1 vertex operators of U_<q,p>(sl^^^_n) implies the basic generating function of the deformed W_<n-1>-algebra.3.The Vertex-Face Correspondence and the Elliptic Quantum groups : By using the vertex-face correspondence in solvable lattices models, we give an explicite correspondence of the representations of the two types of the elliptic quantum groups, the vertex type A_<q,p>(sl^^^_2) and the face type B_<q,λ>(sl^^^_2). Based on this, we give an algebraic analysis formulation of the fusion eight-vertex model.4.The Vertex-Face Correspondence and the Elliptic 6j-symbols : We established a new relationship between the vertex-face correspondence intertwining vectors and the elliptic 6j-symbols. We then simplified a proof of the biorthogonal relation, fusion relation and some other relations of the elliptic 6j-symbols. Especially, we derived an equation characterizing the elliptic 6j-symbol, which is similar to the dynamical RLL-relation of the face type elliptic quantum group B_<q,λ>(sl^^^_2).
1. B_<q,λ>(g)的Drinfeld实现:对于g=A^<(2)>_2,我们用椭圆代数U_<q,p>(g)的流来实现椭圆量子群B_<q,λ>(g)的L-算子。然后证明了同构U_<q,p>(g)=^^B_<q,λ>(g)[叉积] C{H^}是一个结合代数.这里C{H^}表示某个海森堡代数。其次,我们构造了U_q,p>(A^(2)>_2)的一级自由场表示,并证明了U_q,p>(A^(2)>_2)的顶点算子提供了A^(2)>_2 SOS模型的格点算子在代数分析公式中的实现。推广了g=A^(1)>_1,A ^(2)>_2的结果,证明了U_q,p>(sl ^_n)的一对一级顶点算子的融合蕴涵了变形W_ -代数的基本生成函数<n-1>。3.点面对应与椭圆量子群:利用可解格模型中的点-面对应,给出了两类椭圆量子群:点型A_<q,p>(sl ^^^_2)和面型B_<q,λ>(sl ^^^_2)的表示的显式对应.在此基础上,给出了融合八顶点模型的代数分析公式。4.顶点-面对应与椭圆6 j-符号:建立了顶点-面对应交织向量与椭圆6 j-符号之间的新关系。然后简化了椭圆6 j-符号的双正交关系、融合关系等关系的证明。特别地,我们导出了一个描述椭圆6 j-符号的方程,它类似于面型椭圆量子群B_<q,λ>(sl ^^^_2)的动力学RLL-关系.
项目成果
期刊论文数量(80)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Free Field Realisation of the Level 2 Elliptic Algebra U_{x,p}(sl_2^)
2 级椭圆代数 U_{x,p}(sl_2^) 的自由场实现
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:H.Konno;H.Konno;H.Konno;T.Kojima et al.;H.Konno;T.Takebe;H.Boos et al.;B.Feigin et al.;H.Boos et al.;H.Konno;T.Kojima et al.;H.Konno;H.Boos et al.;B.Feigin et al.;H.Boos et al.;T.Takebe;T.Kojima et al.;H.Konno
- 通讯作者:H.Konno
A recursion formula for the correlation functions of an inhomogeneous XXX model,
非齐次 XXX 模型的相关函数的递推公式,
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:Amino;K.;Arai;T.;Sugawara;T.(Editor:Muller;C);進藤 美津子(分担執筆);進藤 美津子;進藤 美津子(分担執筆);進藤 美津子;Jun Mada;S. Isojima;Jun Mada;A. Nishiyama;S. Isojima;Jun Mada;A. Nishiyama;S. Isojima;B. Feigin;A. Kuniba;D. Takahashi;A. Kuniba;A. Kuniba;H. Boos;S. Iwao;F. Lambert;R. Willox;B. Grammaticos;S. Kubo;R. Willox;D. Yanagisawa;Jun Mada;M.Kanai;A.Kuniba;A.Kuniba;H.Inoue;J.Matsukidaira;J.Matsukidaira;T.Tokihiro;M.Kanai;K.Kajiwara;H.Boos
- 通讯作者:H.Boos
Trigonometric degeneration and orbifold Wess-Zumino-Witten model I
三角退化和轨道 Wess-Zumino-Witten 模型 I
- DOI:
- 发表时间:2004
- 期刊:
- 影响因子:0
- 作者:M.Amou;Y.Bugeaud;T.Takebe
- 通讯作者:T.Takebe
The Vertex-Face Correspondence and the Elliptic 6j-symbols
点面对应和椭圆 6j 符号
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:H.Konno;H.Konno;H.Konno
- 通讯作者:H.Konno
The elliptic algebra U_{q,p}(widehat {sl}_N) and the deformation of the W_N algebra
椭圆代数 U_{q,p}(widehat {sl}_N) 和 W_N 代数的变形
- DOI:
- 发表时间:2004
- 期刊:
- 影响因子:0
- 作者:H.Konno;H.Konno;H.Konno;T.Kojima et al.;H.Konno;T.Takebe;H.Boos et al.;B.Feigin et al.;H.Boos et al.;H.Konno;T.Kojima et al.;H.Konno;H.Boos et al.;B.Feigin et al.;H.Boos et al.;T.Takebe;T.Kojima et al.;H.Konno;H.Konno;H.Konno;H.Konno;T.Kojima et al.
- 通讯作者:T.Kojima et al.
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KONNO Hitoshi其他文献
KONNO Hitoshi的其他文献
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{{ truncateString('KONNO Hitoshi', 18)}}的其他基金
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 - 财政年份:2010
- 资助金额:
$ 2.24万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Representations of elliptic quantum groups and their applications to elliptic special functions
椭圆量子群的表示及其在椭圆特殊函数中的应用
- 批准号:
19540033 - 财政年份:2007
- 资助金额:
$ 2.24万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Representation theory of elliptic quantum groups and its application
椭圆量子群的表示论及其应用
- 批准号:
11640030 - 财政年份:1999
- 资助金额:
$ 2.24万 - 项目类别:
Grant-in-Aid for Scientific Research (C)