Cellularité tordue de l'algèbre de Hecke de $G(r,p,n)$


In 1996, Graham and Lehrer introduced the notion of cellular algebra. Graham and Lehrer proved that many known algebras are cellular, for instance: the Ariki-Koike algebra (this includes the Iwahori-Hecke algebras of type A and B), the Brauer algebra, the Temperley-Lieb algebra. Later, using some deep properties of Kazhdan-Lusztig bases Geck proved that the Iwahori-Hecke algebra associated with any finite Coxeter group (or, equivalently, any real reflection group) is cellular. In this talk, following a recent paper in collaboration with Jun Hu and Andrew Mathas I will introduce the notion of skew cellular algebra, which generalises Graham and Lehrer’s definition of cellular algebra. Our main result is that the Hecke algebra associated with any irreducible complex reflection group of the infinite series (that is, all but finitely many irreducible complex reflection groups) is a skew cellular algebra.