irreducible unitary representations of compact groups are finite-dimensional


Theorem - If πrep(G,H) is a unitary representationMathworldPlanetmath of a compact topological group G in a Hilbert spaceMathworldPlanetmath H, then π has a finite-dimensional subrepresentationPlanetmathPlanetmath (http://planetmath.org/TopologicalGroupRepresentation).

Corollary 1 - If π is irreducible (http://planetmath.org/TopologicalGroupRepresentation), then H must be finite-dimensional.

Corollary 2 - π has an .

Title irreducible unitary representations of compact groups are finite-dimensional
Canonical name IrreducibleUnitaryRepresentationsOfCompactGroupsAreFinitedimensional
Date of creation 2013-03-22 18:02:44
Last modified on 2013-03-22 18:02:44
Owner asteroid (17536)
Last modified by asteroid (17536)
Numerical id 13
Author asteroid (17536)
Entry type Theorem
Classification msc 43A65
Classification msc 22C05
Classification msc 22A25
Synonym unitary representation of a compact group has a finite-dimensional subrepresentation
Related topic UnitaryRepresentation
Defines unitary representation of compact group has an irreducible subrepresentation
Defines unitary groupMathworldPlanetmath of a complex Hilbert space