### Abstract

Let H 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 H and Lusztig's a-function, we show that H 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 .

Original language | English |
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Pages (from-to) | 501-517 |

Number of pages | 17 |

Journal | Inventiones Mathematicae |

Volume | 169 |

Issue number | 3 |

Early online date | 1 May 2007 |

DOIs | |

Publication status | Published - Sep 2007 |

### Keywords

- B-N
- representations
- roots
- unity

## Cite this

Geck, M. J. (2007). Hecke algebras of finite type are cellular.

*Inventiones Mathematicae*,*169*(3), 501-517. https://doi.org/10.1007/S00222-007-0053-2