报告题目：Isomorphism between the R-matrix and Drinfeld Presentations of Quantum Affine Algebras

主 讲 人：刘 明

单 位：华南理工大学

时 间：9月5日10:00

腾 讯 ID：972 693 898

密 码：123456

摘 要：

An explicit isomorphism between the R-matrix and Drinfeld presentations of the quantum affine algebra in type A was given by Ding and I. Frenkel (1993). In this talk, we will show that this result can be extended to types B, C and D. In all classical types the Gauss decomposition of the generator matrix in the R-matrix presentation yields the Drinfeld generators. To prove that the resulting map is an isomorphism we follow the work of E. Frenkel and Mukhin (2002) in type A and employ the universal R-matrix to construct the inverse map. A key role in our construction is played by an embedding theorem which allows us to consider the quantum affine algebra of rank n−1 in the R-matrix presentation as a subalgebra of the corresponding algebra of rank n of the same type.

简 介：

刘明，华南理工大学讲师，2019年在澳大利亚悉尼大学从事博士后研究工作。2018年获国家自然科学基金青年科学基金。主要研究方向为量子代数及其表示理论；其主要研究课题为量子Yangian代数，量子仿射代数等。已在国内外权威期刊Comm.Math.Phys.J. Algebra等上发表9篇论文。