Representation theory of elliptic quantum groups and its application

1. 假设局部高度限制为κ + 1，我们分别用顶点算子和q-变形Ζ_κ对偶子理论的基本q-对偶子电流确定了半无限行、列传递矩阵和物理激励的产生算子。我们还证明了模型的尺度极限是由Koberle-Swieca的因式散射理论给出的。<sl>^^^^_2在主级中的表示给出了<sl>^^^^_2在一般级主级中的自由场实现。特别地，我们给出了Lepowsky-Wilson's Ζ-algebra在极限（t = -q^<(k+22)/2>, q→1）下的变形Virasoro代数Vir_<q, t>的自由场实现。基于椭圆量子群β_<q，【lambda bar】>(<sl>^^^^_2)的自由场实现和椭圆代数U_<q, p>(<sl>^^^^_2)，系统构造了β_<q，【lambda bar】>(<sl>^^^^_2)的高自旋纠缠算子。我们还阐明了两个U_q（<sl>^^^^_2）模张量积的协集分解与U_<q, p>(<sl>^^^^_2)的表示之间的关系。

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).