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Solvable Lattice Models and Elliptic Quantum Groups

可解的格子模型和椭圆量子群

基本信息

批准号：
10440042
负责人：
JIMBO Michio
金额：
$ 4.74万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10440042/
关键词：
elliptic quantum groups solvable lattice models free field representation deformed Virasoro algebras conformal field theory invariant theory matrix models 自由場表示頂点作用素相関関数形状因子変形ヴィラソロ代数

项目摘要

Results concerning solvable models and elliptic quantum groups :(1)Fronsdal observed earlier that the elliptic quantum groups are nothing but quasi-Hopf twists of quantum affine algebras. Following this idea, we constructed explicitly the twist defining elliptic quantum groups in the form of an infinite product of the universal R matrix. Our construction settled some conjectures previously made by Foda et al. on vertex type elliptic quantum groups.(2)We obtained an L operator in the Fock space representation and interpreted Lukyanov-Pugai's vertex operators as intertwiners for elliptic quantum groups.(3)We constructed free field representations for solvable lattice models which correspond to integrable perturbations of conformal field theories : the dilute AィイD2LィエD2 models and the ABF models in regime II.Other results :(4)Umeda reformulated and proved Cappelli type identities mentioned by Turnbull, as an identity of invariant differential operators.(5)Shiota showed that ceretain Fredholm determinants arising in the Baker-Akhiezer functions in the KP hierarchy are expressible as ratios of tau functions.(6)Shimizu gave a reformulation of the stress-energy tensorsin conformal field theory as Hamiltonian action on the cotangent bundle of the moduli spaces of Riemann surfaces.

关于可解模型和椭圆量子群的结果：（1）Fronsdal较早地观察到椭圆量子群只不过是量子仿射代数的拟Hopf扭。根据这一思想，我们明确地构造了扭转定义椭圆量子群的形式的无限产品的普遍R矩阵。我们的构造解决了Foda等人以前关于顶点型椭圆量子群的一些问题。(2)We在Fock空间表示中得到了一个L算子，并将Lukyanov-Pugai的顶点算子解释为椭圆量子群的缠绕算子。(3)We构造了对应于共形场论可积扰动的可解格点模型的自由场表示：稀A_（12）D_（2L）D_（2L）D_（2L）模型和区域II的ABF模型.其他结果：（4）Umeda将Turnbull提出的Cappelli型恒等式作为不变微分算子的恒等式重新表述并证明.（5）Shiota证明了KP族中Baker-Akhiezer函数的某些Fredholm行列式可以表示为τ函数的比值。（6）Shimizu将共形场论中的应力-能量张量重新表述为Riemann曲面模空间余切丛上的Hamilton作用量。