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An explicit integral polynomial whose splitting field has Galois group $W (E_{8})$

Florent Jouve; Emmanuel Kowalski; David Zywina — 2008

Journal de Théorie des Nombres de Bordeaux

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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An explicit integral polynomial whose splitting field has Galois group W ( E 8 )

An explicit integral polynomial whose splitting field has Galois group $W (E_{8})$