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Remarks on the wonderful compactification of semisimple algebraic groups

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Abstract

We prove that ifG is a semisimple algebraic group of adjoint type over the field of complex numbers,H is the subgroup of all fixed points of an involution σ ofG that is induced by an involution σ of the simply connected coveringĜ ofG, then the wonderful compactification\(\overline {G/H} \) of the homogeneous spaceG/H is isomorphic to the G.I.T quotientG ss (L)//H of the wonderful compactificationG ofG for a suitable choice of a line bundleL onG. We also prove a functorial property of the wonderful compactifications of semisimple algebraic groups of adjoint type.

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Authors and Affiliations

  1. SPIC Mathematical Institute, 92 G N Chetty Road, T Nagar, 600017, Chennai, India

    S. Senthamarai Kannan

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  1. S. Senthamarai Kannan
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Correspondence to S. Senthamarai Kannan.

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Kannan, S.S. Remarks on the wonderful compactification of semisimple algebraic groups. Proc. Indian Acad. Sci. (Math. Sci.) 109, 241–256 (1999). https://doi.org/10.1007/BF02843529

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  • DOI: https://doi.org/10.1007/BF02843529

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