Exposé d'Emily Norton (Clermont-Ferrand) : Calibrated representations of cyclotomic Hecke algebras at roots of unity

Title: Calibrated representations of cyclotomic Hecke algebras 
at roots of unity 

Abstract: The cyclotomic Hecke algebra is a "higher level" version
 of the Iwahori-Hecke algebra of the symmetric group. It depends on
 a collection of parameters, and its combinatorics involves 
multipartitions instead of partitions. We are interested in the case
 when the parameters are roots of unity. In general, we cannot hope
 for closed-form character formulas of the irreducible representations.
 However, a certain type of representation called "calibrated" is
 more tractable: those representations on which the Jucys-Murphy 
elements act semisimply. We classify the calibrated representations 
in terms of their Young diagrams, give a multiplicity-free formula
 for their characters, and homologically construct them via BGG 
resolutions. This is joint work with Chris Bowman and José Simental.