## Induced representations of groups and quantum mechanics |

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action of G additive group algebra analog analysis angular momentum automorphism Borel function Borel sets Borel space classical mechanics closed subgroup cohomology class commutation relations commutative group compact group coset space countable decomposing decomposition defined denote determined dimensional direct integral direct sum double cosets equivalence class ergodic actions Euclidean group finite Fourier function g G acts G space Galilean group group G group representations Hilbert space identity representation induced representations intertwining operator invariant measure irreducible projective representations irreducible representations Let G linear measure zero Moreover multiplets multiplication obtain one-particle system particle physical projection-valued measure projective representation quantum mechanics quasi-invariant measures real line real numbers regular representation replaced repre representation of G representation of SL(n restriction satisfies the identity self-adjoint operator semidirect product sentation simple groups spectral theorem spin strictly ergodic subgroup H subgroup of G system of imprimitivity tation tensor product transformations uniquely unitary representation vector space virtual subgroup