Journal of Lie Theory Vol. 12, No. 1, pp. 4168 (2002) 

Classification of two Involutions on Compact Semisimple Lie Groups and Root SystemsToshihiko MatsukiToshihiko MatsukiFaculty of Integrated Human Studies Kyoto University Kyoto 6068501, Japan matsuki@math.h.kyotou.ac.jp Abstract: Let ${\frak g}$ be a compact semisimple Lie algebra. Then we first classify pairs of involutions $(\sigma,\tau)$ of ${\frak g}$ with respect to the corresponding double coset decompositions $H\backslash G/L$. (Note that we don't assume $\sigma\tau=\tau\sigma$.) In our paper ``Double coset decompositions of reductive L ie groups arising from two involutions, Journal of Algebra 197 (1997), 4991'' we defined a maximal torus $A$, a (restricted) root system $\Sigma$ and a ``generalized'' Weyl group $J$ and then we proved $$J\backslash A\cong H\backslash G/L$$ when $G$ is connected. In this paper, we also compute $\Sigma$ and $J$ for some representatives of all the pairs of involutions when $G$ is simply connected. By these data, we can compute $\Sigma$ and $J$ for ``all'' the pairs of involutions. Full text of the article:
Electronic fulltext finalized on: 30 Oct 2001. This page was last modified: 9 Nov 2001.
© 2001 Heldermann Verlag
