An explicit integral polynomial whose splitting field has Galois group W(E 8 )
Journal de Théorie des Nombres de Bordeaux, Tome 20 (2008) no. 3, pp. 761-782.

En utilisant le principe selon lequel le polynôme caractéristique de matrices obtenues comme éléments d’un groupe réductif G sur Q a typiquement un corps de décomposition dont le groupe de Galois est le groupe de Weyl de G, nous construisons un polynôme unitaire explicite de degré 240, à coefficients entiers, dont le corps de décomposition a pour groupe de Galois le groupe de Weyl du groupe exceptionnel de type E 8 .

Using the principle that characteristic polynomials of matrices obtained from elements of a reductive group G over Q typically have splitting field with Galois group isomorphic to the Weyl group of G, we construct an explicit monic integral polynomial of degree 240 whose splitting field has Galois group the Weyl group of the exceptional group of type E 8 .

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DOI : https://doi.org/10.5802/jtnb.649
Mots clés : Inverse Galois problem, Weyl group, exceptional algebraic group, random walk on finite group, characteristic polynomial
@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},
     zbl = {pre05572700},
     mrnumber = {2523316},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.649/}
}
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, Tome 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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