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Seminars

Taipei Postdoc Seminar

An Introduction to Crystal Bases for Quantum Groups

2026/06/03 (Wed.) 14:00~15:00
  • Date : 2026/06/03 (Wed.) 14:00~15:00
  • Location : Room 515, Cosmology Building, NTU
  • Speaker : Akito Uruno (NCTS)
  • Organizer : Wille Liu (AS), Harry Richman (NCTS)
  • Abstract : This talk introduces the theory of Crystal Bases, developed by Kashiwara and Lusztig, which serves as a powerful combinatorial tool for understanding the representation theory of Drinfeld-Jimbo quantum groups associated with complex semi-simple Lie algebras. When the quantum parameter $q$ approaches 0, the algebraic structure of a representation naturally simplifies into a combinatorial framework called a "Crystal Graph". In this talk, we explore the framework of crystal bases and demonstrate how they reduce the tensor product decomposition of reducible representations for $gl_{n}$ into the combinatorics of Young tableaux. Finally, we briefly introduce the crystal bases for quantum supergroups, along with a short overview of our recent results concerning the general linear and orthosymplectic cases.
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