The closure of a sheet is not always a union of sheets

Details The closure of a sheet is not always a union of sheets The closure of a sheet is not always a union of sheets

2010-11-23

arxiv.org/abs/1011.5045v1

Mathematics

Representation Theory

short note, 3 pages

Scientific paper

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.

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