Title: Finite dimensional algebras and quantum groups

Speaker: Prof. Jie Du (UNSW)

Abstract: I am going to present an overview of the book with thegiven title. This resaerch/advanced graduate level text combines for the first time in book form the two theories in the title .Note that the book authors form a largest Pacific triangle:Sydney-ShanghaiBeijing-Virginia-Sydney. I will start with (generalized) Cartan matrices and their graphand root datum realizations. With the graph realization, I willdiscuss briefly representations of directed graphs (which arecalled quivers), Gabriel's Theorem and Ringel-Hall algebras. Withthe root datum realization, I will introduce the associatedquantum groups which are regarded as the latest development in Lietheory. I will conclude with the two exciting realizations: TheRingel-Hall algebra realization of the $pm$-part, and the Beilinson-Lusztig-MacPherson realization of the entire quantum $gl_n$ via quantum Schur algebras.

Report time: 2007-07-09 15:00-16:00
Report place: Science Building A508