## Abstract

Let W be the finite Coxeter group of type F_{4}, and H_{r}q be the associated Hecke algebra, with parameter a prime power q, defined over a valuation ring R in a large enough extension field of Q, with residue class field of characteristic r. In this paper, the r-modular decomposition numbers of H_{R}q are determined for all q and r such that r does not divide q. The methods of the proofs involve the study of the generic Hecke algebra of type F_{4} over the ring A = ℤ[u^{1/2}, u^{-1/2}] of Laurent polynomials in an indeterminate u^{1/2} and its specializations onto the ring of integers in various cyclotomic number fields. Substancial use of computers and computer program systems (GAP, MAPLE, Meat-Axe) has been made.

Original language | English (US) |
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Pages (from-to) | 285-306 |

Number of pages | 22 |

Journal | manuscripta mathematica |

Volume | 70 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1991 |

## ASJC Scopus subject areas

- General Mathematics

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