摘要：In this talk, I will give a representation-theoretic proof for the multiplication formula in the Ringel-Hall algebra H∆(n) of a cyclic quiver ∆(n). As a first application, we see immediately the existence of Hall polynomials for cyclic quivers, and derive a recursive formula to compute them. We will further use the formula and the construction of certain monomial base for H∆(n), together with the double Ringel–Hall algebra realisation of the quantum loop algebra, to develop some algorithms and to compute the canonical basis for Uv(gln)^+. As examples, we will show explicitly the part of the canonical basis associated with modules of Lowey length at most 2 for the quantum group Uv(gl2). This talk is based on a joint work with Jie Du.
报告人介绍：赵中华，北京化工大学副教授，硕士生导师。博士毕业于北师大，师从知名代数学专家邓邦明教授。在箭图的表示，Hall代数，量子群等领域作出了一些重要的成果。
