Skew cellularity of the Hecke algebras of type

This paper introduces (graded) skew cellular algebras, which generalise Graham and Lehrer’s algebras. We show that all of the main results from theory algebras extend to we develop a “cellular algebra Clifford theory” for arise as fixed point subalgebras As an application this general theory, result proves Hecke type G ( ℓ , p n stretchy="false">) G(\ell ,p,n) are graded In special case when alttext="p equals 2"> = 2 encoding="application/x-tex">p = 2 implies 2 ,2,n) The proofs these rely, in crucial way, on diagrammatic Cherednik Webster Bowman. Our theorem extends Geck’s one parameter Iwahori-Hecke two ways. First, our applies cyclotomic infinite series Shephard-Todd classification complex reflection groups. Secondly, lift cellularity setting. applications theorem, decomposition matrices unitriangular, construct classify their simple modules prove existence “adjustment matrices” positive characteristic.