(1) Title：Drinfeld realization of the Yangian in type A

Speaker：Prof. Alexander Molev（Sydney University ）

Time: Saturday,January,15,2022， AM：10：00--11:00

Zoom Meeting：818 3937 1417 (https://uni-sydney.zoom.us/j/81839371417)

Or Zoom International No：https://uni-sydney.zoom.us/u/kb8H5Dv0aB

Inviters：Associate Prof. Ming Liu and Prof. Naihuan Jing

Abstract：

    The Yangians form a remarkable family of quantum groups related to rational solutions of the classical Yang--Baxter equation. For each simple finite-dimensional Lie algebra a over the field of complex numbers, the corresponding Yangian Y(a) is a canonical deformation of the universal enveloping algebra U(a[x]) for the polynomial current Lie algebra a[x]. Importantly, the deformation is considered in the class of Hopf algebras which guarantees its uniqueness under some natural `homogeneity' conditions. The representation theory of the Yangians Y(a) is a very much nontrivial and fascinating area. Although the finite-dimensional irreducible representations of Y(a) are classified, their general structure remains largely unknown. The goal of the course is to give an introduction to the Yangian structure theory and their representations, in particular, we will focus on type A.The sixth lecture will continue the discussion of highest weight theory of the Yangian algebra, in particular for type A.

(2) Title：Representations of Yangian algebras of classical types

Time: Saturday,January,22,2022， AM：10：00--11:00

Zoom Meeting：818 3937 417 (https://uni-sydney.zoom.us/j/81839371417)

Or Zoom International No: https://uni-sydney.zoom.us/u/kb8H5Dv0aB

Abstract：

    The Yangians form a remarkable family of quantum groups related to rational solutions of the classical Yang--Baxter equation. For each simple finite-dimensional Lie algebra a over the field of complex numbers, the corresponding Yangian Y(a) is a canonical deformation of the universal enveloping algebra U(a[x]) for the polynomial current Lie algebra a[x]. Importantly, the deformation is considered in the class of Hopf algebras which guarantees its uniqueness under some natural `homogeneity' conditions. The representation theory of the Yangians Y(a) is a very much nontrivial and fascinating area. Although the finite-dimensional irreducible representations of Y(a) are classified, their general structure remains largely unknown. The goal of the course is to give an introduction to the Yangian structure theory and their representations, in particular, we will focus on type A.The seventhth lecture will discuss representation theory of the Yangian algebra in arbitrary type.