The normality of closures of orbits in a Lie algebra |
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| Authors: | Wim Hesselink |
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| Institution: | (1) Hoogbouw WSN, Mathematisch Instituut, Post box 800, Groningen, The Netherlands |
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| Abstract: | LexX be the closure of aG-orbit in the Lie algebra of a connected reductive groupG. It seems that the varietyX is always normal. After a reduction to nilpotent orbits, this is proved for some special cases. Results on determinantal
schemes are used forGl
n
. IfX is small enough we use a resolution and Bott's theorem on the cohomology of homogeneous vector bundles. Our results are conclusive
for groups of typeA
1,A
2,A
3 andB
2. |
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| Keywords: | |
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