The normality of closures of orbits in a Lie algebra
- 1 December 1979
- journal article
- research article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Commentarii Mathematici Helvetici
- Vol. 54 (1), 105-110
- https://doi.org/10.1007/bf02566258
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.Keywords
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