Some properties of orbital varieties in extremal nilpotent orbits

Abstract : The intersection between a nilpotent orbit of a simple Lie algebra and a Borel subalgebra is always equidimensional. Its irreducible components are called orbital varieties. Orbital varieties belonging to different nilpotent orbits may have quite different behaviours. The orbital varieties of the sub-regular nilpotent orbit are always smooth but they have in general infinitely many B-orbits. At the opposite, the minimal nilpotent orbit is spherical but its orbital varieties may have singularities. In this paper, we characterize the orbital varieties of the subregular nilpotent orbit which have a finite number of B-orbits and we give a smoothness criterion for the orbital varieties of the minimal nilpotent orbit.
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Contributor : Lucas Fresse <>
Submitted on : Wednesday, March 21, 2018 - 1:09:17 PM
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Lucas Fresse. Some properties of orbital varieties in extremal nilpotent orbits. 2018. ⟨hal-01739780⟩

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