### 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) |
---|---|

Pages (from-to) | 285-306 |

Number of pages | 22 |

Journal | Manuscripta Mathematica |

Volume | 70 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1991 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

_{ 4}.

*Manuscripta Mathematica*,

*70*(1), 285-306. https://doi.org/10.1007/BF02568379

**The decomposition numbers of the hecke algebra of type F _{ 4}.** / Geck, Meinolf; Lux, Klaus M.

Research output: Contribution to journal › Article

_{ 4}',

*Manuscripta Mathematica*, vol. 70, no. 1, pp. 285-306. https://doi.org/10.1007/BF02568379

_{ 4}. Manuscripta Mathematica. 1991 Dec;70(1):285-306. https://doi.org/10.1007/BF02568379

}

TY - JOUR

T1 - The decomposition numbers of the hecke algebra of type F 4

AU - Geck, Meinolf

AU - Lux, Klaus M

PY - 1991/12

Y1 - 1991/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=51249173111&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249173111&partnerID=8YFLogxK

U2 - 10.1007/BF02568379

DO - 10.1007/BF02568379

M3 - Article

AN - SCOPUS:51249173111

VL - 70

SP - 285

EP - 306

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 1

ER -