Invited by School of Mathematics and Statistics, Ph.D Ming Liu fromSouth China University of Technology will give a lecture online.

Time：3:00 p.m.,Oct.26th, 2021

Conference ID: 439 884 094( Tencent Conference)

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.