Journal of Lie Theory EMIS ELibM Electronic Journals 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 Groups

J.-F. Hämmerli, M. Matthey and U. Suter

J.-F. Hämmerli,
M. Matthey
University of Lausanne
Institute for Geometry, Algebra and Topology (IGAT)
CH-1015 Lausanne,Switzerland,
U. Suter
Institute for Mathematics
University of Neuchâtel
Rue Émile-Argand 11
CH-2007 Neuchâtel, Switzerland

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

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Electronic version published on: 1 Sep 2004. This page was last modified: 1 Sep 2004.

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