Journal of Lie TheoryVol. 14, No. 2, pp. 583--617 (2004)
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Journal of Lie Theory Vol. 14, No. 2, pp. 583--617 (2004) |
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Automorphisms of Normalizers of Maximal Tori and First Cohomology of Weyl GroupsJ.-F. Hämmerli, M. Matthey and U. SuterJ.-F. Hämmerli,M. Matthey University of Lausanne Institute for Geometry, Algebra and Topology (IGAT) BCH CH-1015 Lausanne,Switzerland jean-francois.haemmerli@ima.unil.ch, michel.matthey@ima.unil.ch and U. Suter Institute for Mathematics University of Neuchâtel Rue Émile-Argand 11 CH-2007 Neuchâtel, Switzerland ulrich.suter@unine.ch 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 $H^1(W;T)$ is computed for all simple Lie groups, and the general case is studied. The method is based on a suitable interpretation of $H^1(W;T)$ as a group of (outer) automorphisms of the normalizer of $T$. {\eightsl Full text of the article: Electronic version published on: 1 Sep 2004. This page was last modified: 1 Sep 2004.
© 2004 Heldermann Verlag
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