An explicit integral polynomial whose splitting field has Galois group W(E 8 )
Florent Jouve1 ; Emmanuel Kowalski2 ; David Zywina3
1 Dept. of Mathematics, The University of Texas at Austin 1 University Station C1200 Austin, TX, 78712, USA.
2 ETH Zürich – DMATH Rämistrasse 101 8092 Zürich, Switzerland
3 Department of Mathematics, University of Pennsylvania Philadelphia, PA 19104-6395, USA
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 .

DOI : 10.5802/jtnb.649
Mots clés : Inverse Galois problem, Weyl group, exceptional algebraic group, random walk on finite group, characteristic polynomial
Florent Jouve 1 ; Emmanuel Kowalski 2 ; David Zywina 3

1 Dept. of Mathematics, The University of Texas at Austin 1 University Station C1200 Austin, TX, 78712, USA.
2 ETH Zürich – DMATH Rämistrasse 101 8092 Zürich, Switzerland
3 Department of Mathematics, University of Pennsylvania Philadelphia, PA 19104-6395, USA 
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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, 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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