Complex sentence: Schur indicator describes what invariant bilinear forms a given irreducible representation of a compact group on a complex vector space has, and can be used to classify the irreducible representations of compact groups on real vector spaces.
Split into simpler sentences: Schur indicator describes what invariant bilinear forms a given irreducible representation of a compact group on a complex vector space has. It can be used to classify the irreducible representations of compact groups on real vector spaces.