When is an orbit defined by the natural action of Lie subgroup of GL(n,C) a manifold?

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[email protected] [email protected] facultad de matematicas uv xalapa

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Raul Alvarez

Why you claim that the orbit is immersed? It is posible to have an action such that is constant when is restricted to the given subgroup. Take for example U(1) < GL(1,C). Then 0 is a fixed point of the U(1)-action (actually it is a fixed point of the whole action) induced by the foundamental representation of GL(1,C) in C.

Danish Hasnat

can there be a sheaf with GL(n,C) and the projection of this sheaf onto a C^n manifold have orbits which are closed and thus have a natural identification as a manifold.