Observable subgroup
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In mathematics, in the representation theory of algebraic groups, an algebraic subgroup of an algebraic linear group is termed observable if every finite dimensional rational representation of the subgroup arises as the restriction to the subgroup of a finite dimensional rational representation of the whole group.
An equivalent formulation, in case the base field is closed, is that K is an observable subgroup of G if and only if the quotient variety G / K is a quasi affine variety.
Other equivalent formulations Some basic facts about observable subgroups:
- Any normal algebraic subgroup of an algebraic group is observable.
- Any observable subgroup of an observable subgroup is observable.
