An explicit integral polynomial whose splitting field has Galois group W(E_8)

Florent Jouve (1) , E. Kowalski (1, 2) , D. Zywina

1 IMB - Institut de Mathématiques de Bordeaux
2 Laboratoire de mathématiques

Using the principle that characteristic polynomials of matrices obtained from elements of a reductive group over a number field typically have splitting field with Galois group isomorphic to its Weyl group, 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.

Domaines: Théorie des nombres [math.NT]; Théorie des groupes [math.GR]

Florent Jouve, E. Kowalski, D. Zywina. An explicit integral polynomial whose splitting field has Galois group W(E_8). Journal de Théorie des Nombres de Bordeaux, 2009, Volume en l'honneur de Henri Cohen. ⟨hal-00387294⟩