A theorem on extending representations
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- by Raymond C. Fabec PDF
- Proc. Amer. Math. Soc. 75 (1979), 157-162 Request permission
Abstract:
We obtain sufficient conditions for a unitary representation of a closed subgroup M of a separable locally compact group G to have a unique unitary extension to G. The conditions depend on the behavior of the representation on a closed normal subgroup N of G contained in M. We then discuss an application of the theorem in particle physics.References
- Raymond C. Fabec, Free particle systems and their dynamics in de Sitter space, J. Mathematical Phys. 18 (1977), no. 11, 2087–2091. MR 459476, DOI 10.1063/1.523185
- George W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. (2) 55 (1952), 101–139. MR 44536, DOI 10.2307/1969423
- George W. Mackey, The theory of unitary group representations, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill.-London, 1976. Based on notes by James M. G. Fell and David B. Lowdenslager of lectures given at the University of Chicago, Chicago, Ill., 1955. MR 0396826
- George W. Mackey, Unitary representations of group extensions. I, Acta Math. 99 (1958), 265–311. MR 98328, DOI 10.1007/BF02392428
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 157-162
- MSC: Primary 22D10
- DOI: https://doi.org/10.1090/S0002-9939-1979-0529233-X
- MathSciNet review: 529233