CCNU 代数学系列报告 (四)：Isomorphism between the R-matrix and Drinfeld Presentations of Quantum Affine Algebras

发布时间：2022-11-10 来源：赢咖3 浏览次数：

Speaker:	刘明	DateTime:	2022年11月11日（周五）14:30-15：30
Brief Introduction to Speaker: 刘明，华南理工大学赢咖3副教授。研究方向：李代数、量子群。在Com. Math. Phy., Contemp. Math., J. Algebra 等高水平杂志上发表十多篇学术论文。		Place:	腾讯会议 : 31815304736
Abstract: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.