On the reality of complex reflection groups (and their associated Hecke algebras)

Dr. Maria Chlouveraki

23 September 2022 17:00

Abstract

Real reflection groups are the groups of symmetry of real-life objects, and their Hecke algebras appear naturally in the study of finite algebraic groups. Real reflection groups are particular cases though of complex reflection groups, whose Hecke algebras were defined by Broué, Malle and Rouquier over 20 years ago, and have since become a subject of research in their own right. Even though numerous results in the past two decades indicate that these objects behave in the complex case similarly to the real one, most of their properties are hard to prove and demand a case-by-case analysis. Symbolic computation has been a powerful ally to representation theorists, and in this talk we will discuss how it was used to prove some of the most fundamental conjectures concerning the structure of Hecke algebras associated with complex reflection groups.