Abstract
In this chapter, we study non semisimple Iwahori-Hecke algebras in the spirit of Brauer’s classical modular representation theory. Using Lusztig’s a-function, we define the key concept of “canonical basic set”. This concept gives a theoritical way to classify the simple modules of Iwahori-Hecke algebras at roots of unity. It is in particular independent of the notion of cellular structure. We develop a general strategy to determine explicitly the canonical basic sets for Iwahori-Hecke algebras of classical types. A model case is given by the symmetric group. In another direction, we present a factorisation result for decomposition matrices and present a general formulation of James’ conjecture.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
