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Representation theory of elliptic quantum groups and its application

椭圆量子群的表示论及其应用

基本信息

批准号：
11640030
负责人：
KONNO Hitoshi
金额：
$ 2.37万
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：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640030/
关键词：
elliptic quantum group solvable lattice model affine Lie algebra parafermion quantum group elliptic function 量子群アフィンリー環アフィンリー環可積分系頂点作用素 W-代数共形場理論 q-変形散乱理論

项目摘要

1. Formulation of the ABF model in regime II in terms of the vertex operatorsSupposing the local height restriction is κ + 1, we have identified the half-infinite row and column transfer matrices and the creation operator of the physical excitation with the vertex operators and the basic q-parafermion currents of the q-deformed Ζ_κ parafermion theory, respectively. We have also shown that the scaling limit of the model is given by Koberle-Swieca's factorized scattering theory.2. Representation of <sl>^^^^_2 in the principal gradationWe have given a free field realization of the representation of <sl>^^^^_2 in the generic level principal gradation. Especially, we have given a free field realization of Lepowsky-Wilson's Ζ-algebra as the deformed Virasoro algebra Vir_<q, t> in the limit (t = -q^<(k+22)/2>, q → 1).3. Higher level representation of the elliptic quantum group β_<q,【lambda bar】>(<sl>^^^^_2)Based on the free field realization of β_<q,【lambda bar】>(<sl>^^^^_2) and the elliptic algebra U_<q, p>(<sl>^^^^_2), we have given a systematic construction of the higher spin intertwining operators of β_<q,【lambda bar】>(<sl>^^^^_2). We have also clarified a relation between the coset decomposition of the tensor product of two U_q(<sl>^^^^_2)-modules and the representation of U_<q, p>(<sl>^^^^_2).

1.在局域高度限制为κ + 1的情况下，我们用顶点算符和q-变形的κ_κ仿费米子理论的基本q-仿费米子流分别确定了半无限行列转移矩阵和物理激发的产生算符。我们还证明了模型的标度极限由Koberle-Swieca的因子化散射理论给出.本文<sl>给出了^_2在<sl>类水平主灰度中的自由场表示。特别地，我们给出了Lepowsky-Wilson代数的一个自由场实现，即变形Virasoro代数Vir_<q，t>在极限（t = -q^<（k+22）/2>，q → 1）上的自由场实现.椭圆量子群β_<q，[lambda bar]>（^^^^_2）的高阶表示<sl>基于β_<q，[lambda bar]>（^^^^^_2）的自由场实现<sl>和椭圆代数U_<q，p>（<sl>^^^^_2），我们系统地构造了β_<q，[lambda bar]>（^^^^^_2）的高阶自旋纠缠算符<sl>.我们还阐明了两个U_q（^_2）-模的张量积的陪集分解<sl>与U_<q，p>（^_2）的表示之间的关系<sl>。