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 = {Jouve, Florent and Kowalski, Emmanuel and Zywina, David}, 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 = {http://www.numdam.org/articles/10.5802/jtnb.649/} }
TY - JOUR AU - Jouve, Florent AU - Kowalski, Emmanuel AU - Zywina, David 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 - http://www.numdam.org/articles/10.5802/jtnb.649/ DO - 10.5802/jtnb.649 LA - en ID - JTNB_2008__20_3_761_0 ER -
%0 Journal Article %A Jouve, Florent %A Kowalski, Emmanuel %A Zywina, David %T An explicit integral polynomial whose splitting field has Galois group $W(\mathbf{E}_8)$ %J Journal de théorie des nombres de Bordeaux %D 2008 %P 761-782 %V 20 %N 3 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.649/ %R 10.5802/jtnb.649 %G en %F JTNB_2008__20_3_761_0
Jouve, Florent; Kowalski, Emmanuel; Zywina, David. 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. http://www.numdam.org/articles/10.5802/jtnb.649/
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