### 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 |
---|---|

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

*Inventiones Mathematicae*,

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

**Hecke algebras of finite type are cellular.** / Geck, Meinolf Josef.

Research output: Contribution to journal › Article

*Inventiones Mathematicae*, vol. 169, no. 3, pp. 501-517. https://doi.org/10.1007/S00222-007-0053-2

}

TY - JOUR

T1 - Hecke algebras of finite type are cellular

AU - Geck, Meinolf Josef

PY - 2007/9

Y1 - 2007/9

N2 - 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 .

AB - 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 .

KW - B-N

KW - representations

KW - roots

KW - unity

U2 - 10.1007/S00222-007-0053-2

DO - 10.1007/S00222-007-0053-2

M3 - Article

VL - 169

SP - 501

EP - 517

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

IS - 3

ER -