The twisted quantum affine algebra $U_q(A^{(2)_2)$ and correlation functions of the Izergin-Korepin model

Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis

We analyze wavefunctions of the six-vertex model by extending the Izergin-Korepin analysis on the domain wall boundary partition functions. We particularly focus on the case with triangular boundary. By using the $U_q(sl_2)$ $R$-matrix and a special class of the triangular $K$-matrix, we first introduce an analogue of the wavefunctions of the integrable six-vertex model with triangular boundary. We first give a characterization of the wavefunctions by extending our recent work of the Izergin-Korepin analysis of the domain wall boundary partition function with triangular boundary, and then dete…

量子齐次代数$U_q(\widehat{\mathfrak{gl}}_N)$的多重交换关系，嵌套Bethe向量与Gelfand-Tsetlin基

Multiple commutation relations of the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_N)$, nested Bethe vector and the Gelfand-Tsetlin basis

本文研究了量子齐次代数$U_q(\widehat{\mathfrak{gl}}_N)$的多重交换关系，推导了向量表示的Gelfand-Tsetlin基构造方法，并探讨了其与Bethe向量的关系。