Free Field Approach to Elliptic Quantum Groups : Vertex Operator and T-Q Operator

我们研究了以下两个问题：(1)对角化与量子群UQ(A2(2))、UQ(HAT{sl}(M|N))和椭圆量子群UQP(HAT{sl}N)有关的自旋链的哈密顿量。我们研究了具有三角形边界(Uq(Hat{sl}_2)对称性)的XXZ链，得到了关联函数的积分表示(与P.Baseilhac共同工作)。(2)我们构造了Uq(\Hat{sl}(N|1))的自由场实现，对于任意水平k(复数)。我们构造了筛选和顶点算子的自由场实现。引入了椭圆超代数UQP(Hat{sl}(M|N))，给出了任意k阶的UQP(Hat{sl}(N|1))的自由域实现.

We study the following 2 problems.(1) We diagonalize the Hamiltonian of spin chains associated with quantum group Uq(A_2(2)), Uq(\hat{sl}(M|N)), and elliptic quantum group Uqp(\hat{sl}_N). We study XXZ chain with a triangular boundary (Uq(\hat{sl}_2) symmetry), and derive integral representations of correlation functions (Joint work with P.Baseilhac).(2) We construct a free field realization of Uq(\hat{sl}(N|1)) for an arbitrary level k ( complex number). We constructed free field realizations of screenings and vertex operators. We introduce the elliptic super-algebra Uqp(\hat{sl}(M|N)), and give a free field realization of Uqp(\hat{sl}(N|1)) for an arbitrary level k.