伴随根系An (或等价地，对酉群的U(n+1))以及Cn 、Dn 产生的多变量基本超几何级数，在组合论、数论、李代数表示论、量子代数理论、偏微分方程等领域都有重要的应用，是现代数学研究的重要课题。本项目计划以Bailey格、反演技术、指数算子、行列式计算等为基本方法，研究U(n+1)、Cn、Dn基本超几何级数及其相关问题，建立一批创新性的重要结果，特别是给出著名的Agarwal-Andrews-Bressoud Bailey格以及其它著名结果的多变量拓广及其进一步应用，并且寻求新的方法和思想，从更高层次探索多变量基本超几何级数理论的突破；以及通过深入研究Theta与椭圆函数，开展Theta函数与椭圆型基本超几何级数的研究。本项目目标是建立系统的方法，使我们的研究上一个台阶，取得前沿领域的创新性研究成果，促使多变量基本超几何级数研究在国内的发展，建设好我们的学术梯队。

With the root systems An ( or equivalently, the unitary group U(n+1)) and Cn, Dn, the multivariate basic hypergeometric series which has important applications in combinatorics, number theory, Li algebra representation, quantum algebra theory, partial differential equations and other fields, is an important subject of modern mathematics research. By applying Bailey chain, inverse technique,exponential operator,determinant calculation，etc., this project will research U(n+1), Cn, Dn basic hypergeometric series and related problems to establish a number of innovative and important results, specially, the multivariate extensions and further applications of the well-known Agarwal-Andrews-Bressoud Bailey lattice and other well-known results. By seeking new methods and ideas, the progress of the multivariate basic hypergeometric series will be explored at a higher leverl, and through in-depth study of Theta and elliptic functions, basic hypergeometric series of elliptic type and Theta functions will be researched. The goal of this project is to establish the systematic method, to obtain achievements frontiers,and construct the academic echelon to make our academic achievements to a new step, so that the multivariate basic hypergeometric series will have further development in China.