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Journal of Lie Theory 12 (2002), No. 2, 357--368
Copyright Heldermann Verlag 2002

The Outer Automorphism Group of Normalizers of Maximal Tori in Connected Compact Lie Groups

Jean-François Hämmerli
Dept. of Mathematics, Faculty of Science, Okayama University, 3-1 Tsushima-naka, 700-8530 Okayama, Japan

Let G be a connected compact Lie group, T a maximal torus of G, N = NG(T) its normalizer and W = N/T the Weyl group of G. We show that the outer automorphism group of N canonically decomposes as a semidirect product, where the normal subgroup is given by the cohomology group H1(W; T).

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