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单词 IrreducibleUnitaryRepresentationsOfCompactGroupsAreFinitedimensional
释义

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 .

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更新时间:2025/5/3 13:40:40