Speaker: Pro.Seok-Jin Kang（University of the United Arab Emirates）

Title: LECTURES ON LIE ALGEBRAS

Time: Tues, May.7, 2019, AM:8:30-12:00

         Wed, May.8, 2019, AM:8:30-12:00

         Thur,May.9, 2019, AM:8:30-12:00

         Fri,May.10, 2019, AM:8:30-12:00

Location: Room 4318, Building No.4, Wushan Campus

Abstract:

     In this series of lectures, we will give an introduction to Lie algebras and their representation theory. If time permitting, we will give a brief touch of quantum groups and crystal bases. Here is the plan of my lectures.

      1．Basic linear algebra

      2．De_nition and examples of Lie algebras

      3．Nilpotent, solvable and semisimple Lie algebras

      4． Representation of Lie algebras

      5．Complete reducibility: Weyl's theorem

      6．sl2 representation theory

      7．Root system

      8．Classi_cation of _nite dimesional complex semisimple Lie algebras

      9．PBW theorem

      10．Serre's presentation

      11．Highest weight modules

      12．Quantum sln, crystal bases and Young tableaux