Automorphisms of Normalizers of Maximal Tori and First Cohomology of Weyl Groups

J.-F. Hämmerli; M. Matthey; U. Suter

doi:10.5802/jolt.355

J.-F. Hämmerli; M. Matthey; U. Suter

Journal of Lie Theory, Volume 14 (2004) no. 2, pp. 583-617

Abstract

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.

Zbl

DOI: 10.5802/jolt.355

Classification: 20J06, 22E15, 22D45
Keywords: Cohomology of Weyl groups, compact Lie groups, normalizers of maximal tori, outer automorphisms

@article{JOLT_2004_14_2_a15,
     author = {J.-F. H\"ammerli and M. Matthey and U. Suter},
     title = {Automorphisms of {Normalizers} of {Maximal} {Tori} and {First} {Cohomology} of {Weyl} {Groups<!--} {Anfang} {Autor} -->},
     journal = {Journal of Lie Theory},
     pages = {583--617},
     year = {2004},
     volume = {14},
     number = {2},
     doi = {10.5802/jolt.355},
     zbl = {1092.22004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.355/}
}

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J.-F. Hämmerli; M. Matthey; U. Suter. Automorphisms of Normalizers of Maximal Tori and First Cohomology of Weyl Groups. Journal of Lie Theory, Volume 14 (2004) no. 2, pp. 583-617. doi: 10.5802/jolt.355

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