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• W2079804101 abstract "We give a generalization of the Cartan decomposition for connected compact Lie groups motivated by the work on visible actions of T. Kobayashi [J. Math. Soc. Japan, 2007] for type A group. This paper extends his results to type D group. First, we classify a pair of Levi subgroups $(L,H)$ of a simple compact Lie group $G$ of type D such that $G=LG^{sigma}H$ where $sigma$ is a Chevalley–Weyl involution. This gives the visibility of the $L$-action on the generalized flag variety $G/H$ as well as that of the $H$-action on $G/L$ and of the $G$-action on $(Gtimes G)/(Ltimes H)$. Second, we find a generalized Cartan decomposition $G=LBH$ with $B$ in $G^{sigma}$ by using the herringbone stitch method which was introduced by Kobayashi in his 2007 paper. Applications to multiplicity-free theorems of representations are also discussed." @default.
• W2079804101 created "2016-06-24" @default.
• W2079804101 creator A5071471877 @default.
• W2079804101 date "2013-07-01" @default.
• W2079804101 modified "2023-10-03" @default.
• W2079804101 title "Visible actions on flag varieties of type D and a generalization of the Cartan decomposition" @default.
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• W2079804101 doi "https://doi.org/10.2969/jmsj/06530931" @default.
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