### Abstract

Original language | English |
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Pages (from-to) | 653-677 |

Number of pages | 25 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 52 |

Issue number | 3 |

Early online date | 23 Sep 2009 |

DOIs | |

Publication status | Published - Oct 2009 |

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### Cite this

*Proceedings of the Edinburgh Mathematical Society*,

*52*(3), 653-677. https://doi.org/10.1017/S0013091508000394

**Leading coefficients and cellular bases of Hecke algebras.** / Geck, Meinolf.

Research output: Contribution to journal › Article

*Proceedings of the Edinburgh Mathematical Society*, vol. 52, no. 3, pp. 653-677. https://doi.org/10.1017/S0013091508000394

}

TY - JOUR

T1 - Leading coefficients and cellular bases of Hecke algebras

AU - Geck, Meinolf

PY - 2009/10

Y1 - 2009/10

N2 - Let H be the generic Iwahori–Hecke algebra associated with a finite Coxeter group W. Recently, we have shown that H admits a natural cellular basis in the sense of Graham and Lehrer, provided that W is a Weyl group and all parameters of H are equal. The construction involves some data arising from the Kazhdan–Lusztig basis {Cw} of H and Lusztig's asymptotic ring J}. We attempt to study J and its representation theory from a new point of view. We show that J can be obtained in an entirely different fashion from the generic representations of H, without any reference to {Cw}. We then extend the construction of the cellular basis to the case where W is not crystallographic. Furthermore, if H is a multi-parameter algebra, we see that there always exists at least one cellular structure on H. Finally, the new construction of J may be extended to Hecke algebras associated with complex reflection groups.

AB - Let H be the generic Iwahori–Hecke algebra associated with a finite Coxeter group W. Recently, we have shown that H admits a natural cellular basis in the sense of Graham and Lehrer, provided that W is a Weyl group and all parameters of H are equal. The construction involves some data arising from the Kazhdan–Lusztig basis {Cw} of H and Lusztig's asymptotic ring J}. We attempt to study J and its representation theory from a new point of view. We show that J can be obtained in an entirely different fashion from the generic representations of H, without any reference to {Cw}. We then extend the construction of the cellular basis to the case where W is not crystallographic. Furthermore, if H is a multi-parameter algebra, we see that there always exists at least one cellular structure on H. Finally, the new construction of J may be extended to Hecke algebras associated with complex reflection groups.

U2 - 10.1017/S0013091508000394

DO - 10.1017/S0013091508000394

M3 - Article

VL - 52

SP - 653

EP - 677

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 3

ER -