%0 Journal Article %1 Geck1991 %A Geck, Meinolf %A Lux, Klaus %D 1991 %J manuscripta mathematica %K from:meinolfgeck from:geck %N 1 %P 285--306 %R 10.1007/BF02568379 %T The decomposition numbers of the Hecke algebra of type F4 %U https://doi.org/10.1007/BF02568379 %V 70 %X LetW be the finite Coxeter group of typeF4, andHr(q) be the associated Hecke algebra, with parameter a prime powerq, defined over a valuation ringR in a large enough extension field ofQ, with residue class field of characteristicr. In this paper, ther-modular decomposition numbers ofHR(q) are determined for allq andr such thatr does not divideq. The methods of the proofs involve the study of the generic Hecke algebra of typeF4over the ringA = ℤu1/2,u-1/2 of Laurent polynomials in an indeterminateu1/2 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.

@article{Geck1991, abstract = {LetW be the finite Coxeter group of typeF4, andHr(q) be the associated Hecke algebra, with parameter a prime powerq, defined over a valuation ringR in a large enough extension field ofQ, with residue class field of characteristicr. In this paper, ther-modular decomposition numbers ofHR(q) are determined for allq andr such thatr does not divideq. The methods of the proofs involve the study of the generic Hecke algebra of typeF4over the ringA = ℤ[u1/2,u-1/2] of Laurent polynomials in an indeterminateu1/2 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.}, added-at = {2021-07-11T12:04:46.000+0200}, author = {Geck, Meinolf and Lux, Klaus}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/21aef850b19656cc14dd801f0504a5b5e/mathematik}, day = 01, doi = {10.1007/BF02568379}, interhash = {a5c2234edf3743bbd3f4346fa43ead01}, intrahash = {1aef850b19656cc14dd801f0504a5b5e}, issn = {1432-1785}, journal = {manuscripta mathematica}, keywords = {from:meinolfgeck from:geck}, month = dec, number = 1, pages = {285--306}, timestamp = {2021-07-11T10:04:46.000+0200}, title = {The decomposition numbers of the Hecke algebra of type F4}, url = {https://doi.org/10.1007/BF02568379}, volume = 70, year = 1991 }