The closure of a sheet is not always a union of sheets, a short note

Abstract : In this note we answer to a frequently asked question. If G is an algebraic group acting on a variety V, a G-sheet of V is an irreducible component of V^(m), the set of elements of V whose G-orbit has dimension m. We focus on the case of the adjoint action of a semisimple group on its Lie algebra. We give two families of examples of sheets whose closure is not a union of sheets in this setting.
Keywords : sheet Lie algebra
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https://hal.archives-ouvertes.fr/hal-00660584
Contributor : Michael Bulois <>
Submitted on : Friday, March 29, 2019 - 10:57:47 AM
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Michael Bulois. The closure of a sheet is not always a union of sheets, a short note. 2015. ⟨hal-00660584v2⟩

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