Analysis of the solution space for the quantum KZ equation and its applications to integrable systems

点击翻译按钮获取中文摘要

We get two results about related problems to the quantum Knizhnik-Zamolodchikov equation. First, we constructed an algebra which describes the multiplication structure of a family of q-series containing a q-analogue of multiple zeta values. A family of linear relations called the double shuffle relations is formulated and proved in our framework. Second, we defined a discrete analogue of the Hamiltonian of the non-ideal Bose gas with delta-potentials, and constructed eigenfunctions by means of the Bethe ansatz method making use of a representation of the affine Hecke algebra.