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

Details 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)

2008-01-11

arxiv.org/abs/0801.1733v1

Mathematics

Number Theory

18 pages

Scientific paper

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.

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