Hecke algebras of finite type are cellular

Details Hecke algebras of finite type are cellular Hecke algebras of finite type are cellular

2006-11-30

arxiv.org/abs/math/0611941v3

Mathematics

Representation Theory

14 pages; added references

Scientific paper

10.1007/s00222-007-0053-2

Let $\cH$ 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 $\cH$ and Lusztig's $\ba$-function, we show that $\cH$ 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 $B_n$.

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