Hecke algebras of finite type are cellular

Let be the one-parameter Hecke algebra associated to a finite Weyl group W, defined over a ground ring in which “bad” primes for W are invertible. Using deep properties of the Kazhdan–Lusztig basis of and Lusztig’s a-function, we show that has a natural cellular structure in the sense of Graham and Lehrer. Thus, we obtain a general theory of “Specht modules” for Hecke algebras of finite type. Previously, a general cellular structure was only known to exist in types A _n and B _n .