Using the principle that characteristic polynomials of matrices obtained from elements of a reductive group over typically have splitting field with Galois group isomorphic to the Weyl group of , we construct an explicit monic integral polynomial of degree whose splitting field has Galois group the Weyl group of the exceptional group of type .
En utilisant le principe selon lequel le polynôme caractéristique de matrices obtenues comme éléments d’un groupe réductif sur a typiquement un corps de décomposition dont le groupe de Galois est le groupe de Weyl de , nous construisons un polynôme unitaire explicite de degré , à coefficients entiers, dont le corps de décomposition a pour groupe de Galois le groupe de Weyl du groupe exceptionnel de type .
@article{JTNB_2008__20_3_761_0,
author = {Florent Jouve and Emmanuel Kowalski and David Zywina},
title = {An explicit integral polynomial whose splitting field has {Galois} group $W(\mathbf{E}_8)$},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {761--782},
publisher = {Universit\'e Bordeaux 1},
volume = {20},
number = {3},
year = {2008},
doi = {10.5802/jtnb.649},
mrnumber = {2523316},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.649/}
}
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AU - Florent Jouve
AU - Emmanuel Kowalski
AU - David Zywina
TI - An explicit integral polynomial whose splitting field has Galois group $W(\mathbf{E}_8)$
JO - Journal de théorie des nombres de Bordeaux
PY - 2008
SP - 761
EP - 782
VL - 20
IS - 3
PB - Université Bordeaux 1
UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.649/
UR - https://www.ams.org/mathscinet-getitem?mr=2523316
UR - https://doi.org/10.5802/jtnb.649
DO - 10.5802/jtnb.649
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Florent Jouve; Emmanuel Kowalski; David Zywina. An explicit integral polynomial whose splitting field has Galois group $W(\mathbf{E}_8)$. Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 3, pp. 761-782. doi : 10.5802/jtnb.649. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.649/
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