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

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

Journal de Théorie des Nombres de Bordeaux (2008)

  • Volume: 20, Issue: 3, page 761-782
  • ISSN: 1246-7405

Abstract

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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 .

How to cite

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Jouve, Florent, Kowalski, Emmanuel, and Zywina, David. "An explicit integral polynomial whose splitting field has Galois group $W(\mathbf{E}_8)$." Journal de Théorie des Nombres de Bordeaux 20.3 (2008): 761-782. <http://eudml.org/doc/10859>.

@article{Jouve2008,
abstract = {Using the principle that characteristic polynomials of matrices obtained from elements of a reductive group $\mathbf\{G\}$ over $\mathbf\{Q\}$ typically have splitting field with Galois group isomorphic to the Weyl group of $\mathbf\{G\}$, 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 $\mathbf\{E\}_8$.},
affiliation = {Dept. of Mathematics, The University of Texas at Austin 1 University Station C1200 Austin, TX, 78712, USA.; ETH Zürich – DMATH Rämistrasse 101 8092 Zürich, Switzerland; Department of Mathematics, University of Pennsylvania Philadelphia, PA 19104-6395, USA},
author = {Jouve, Florent, Kowalski, Emmanuel, Zywina, David},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Inverse Galois problem; Weyl group; exceptional algebraic group; random walk on finite group; characteristic polynomial; inverse Galois problem},
language = {eng},
number = {3},
pages = {761-782},
publisher = {Université Bordeaux 1},
title = {An explicit integral polynomial whose splitting field has Galois group $W(\mathbf\{E\}_8)$},
url = {http://eudml.org/doc/10859},
volume = {20},
year = {2008},
}

TY - JOUR
AU - Jouve, Florent
AU - Kowalski, Emmanuel
AU - Zywina, David
TI - An explicit integral polynomial whose splitting field has Galois group $W(\mathbf{E}_8)$
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2008
PB - Université Bordeaux 1
VL - 20
IS - 3
SP - 761
EP - 782
AB - Using the principle that characteristic polynomials of matrices obtained from elements of a reductive group $\mathbf{G}$ over $\mathbf{Q}$ typically have splitting field with Galois group isomorphic to the Weyl group of $\mathbf{G}$, 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 $\mathbf{E}_8$.
LA - eng
KW - Inverse Galois problem; Weyl group; exceptional algebraic group; random walk on finite group; characteristic polynomial; inverse Galois problem
UR - http://eudml.org/doc/10859
ER -

References

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