Observable subgroup
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In mathematics, in the representation theory of algebraic groups, an algebraic subgroup of a linear algebraic 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.
