Geodesic
Automorphisms of Normalizers of Maximal Tori and First Cohomology of Weyl Groups
Journal of Lie theory, Tome 14 (2004) no. 2, pp. 583-617.

Voir la notice de l'article provenant de la source Heldermann Verlag

Let T be a maximal torus in a connected compact Lie group G, and let W be the corresponding Weyl group with its natural action on T as a reflection group. The cohomology group H1(W; T) is computed for all simple Lie groups, and the general case is studied. The method is based on a suitable interpretation of H1(W; T) as a group of (outer) automorphisms of the normalizer of T.
Classification : 20J06, 22E15, 22D45
Mots-clés : Cohomology of Weyl groups, compact Lie groups, normalizers of maximal tori, outer automorphisms 
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     author = {J.-F. H�mmerli and M. Matthey and U. Suter},
     title = {Automorphisms of {Normalizers} of {Maximal} {Tori} and {First} {Cohomology} of {Weyl} {Groups}},
     journal = {Journal of Lie theory},
     pages = {583--617},
     publisher = {mathdoc},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/JLT_2004_14_2_JLT_2004_14_2_a15/}
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J.-F. H�mmerli; M. Matthey; U. Suter. Automorphisms of Normalizers of Maximal Tori and First Cohomology of Weyl Groups. Journal of Lie theory, Tome 14 (2004) no. 2, pp. 583-617. http://geodesic.mathdoc.fr/item/JLT_2004_14_2_JLT_2004_14_2_a15/