Remarks on the wonderful compactification of semisimple algebraic groups |
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Authors: | S. Senthamarai Kannan |
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Affiliation: | (1) SPIC Mathematical Institute, 92 G N Chetty Road, T Nagar, 600017 Chennai, India |
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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 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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Keywords: | Involution wonderful compactification symmetric varieties special dominant weight line bundle |
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