Journal of Lie Theory Vol. 14, No. 2, pp. 583617 (2004) 

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 CH1015 Lausanne,Switzerland jeanfrancois.haemmerli@ima.unil.ch, michel.matthey@ima.unil.ch and U. Suter Institute for Mathematics University of Neuchâtel Rue ÉmileArgand 11 CH2007 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
