Groups and Operator Algebras Seminar

Speaker: Sven Raum (Stockholm University)

Title: On the structure of Iwahori-Hecke (operator) algebras

Abstract: Given a Coxeter system, a commutative ring and a suitable deformation parameter, one can introduce an Iwahori-Hecke algebra. When considered over the complex numbers, these algebras can be completed to C*-algebras and von Neumann algebras in a natural way. Basic questions from representation theory require us to describe their structure. For spherical and affine Hecke algebras, this problem has been studied for a long time and has a satisfactory answer. For Coxeter systems of indefinite type however, a lack of tools from combinatorics, commutative algebra and algebraic geometry obstructed progress until about 15 years ago. In their place, geometric group theory and operator algebras played a key role in recent advances on the topic.

After an introduction to Coxeter systems and Hecke (operator) algebras, I will describe their role in representation theory and present results on their factor decomposition, simplicity and their centre. This talk includes joint work with Adam Skalski as well as joint work with Timothée Marquis.

GOA website: https://sites.google.com/view/copenhagen-goa-seminar