报告人： 杜杰教授 (University of New South Wales, Australia)
报告时间：2025年6月23日-6月27日上午9:30-11:00
报告地点：维格堂119教室
摘要： Reflection groups are groups generated by reflections. Important reflection groups include the group of isometries in Euclidean geometry and the Weyl groups in Lie theory. Finite Weyl groups are used to determine the BN structure of the associated semi-simple Lie or algebraic groups. Reflection groups are Coxeter groups. As natural deformation of Coxeter group algebras, Hecke algebras are fundamentally important in representation theories of semi-simple algebraic groups or Lie algebras and finite groups of Lie type. Since 1990s, Hecke algebras have been seen as a key player in finding the structural properties of the corresponding quantum groups or i-quantum groups. In this lecture series, I will present the basic theory of Hecke algebras. This includes their natural bases, canonical bases, algebraic symmetry, semi-simplicity, Kazhdan-Lusztig cell theory, and their associated q-Schur algebras for classical types. If time permits, I will also show how quantum groups are constructed via $q$-Schur algebras and how canonical bases are built from Hecke algebras to quantum groups via again q-Schur algebras.
邀请人：吕仁才