Square-integrable representations and the Mackey theory
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- by Terje Sund
- Trans. Amer. Math. Soc. 194 (1974), 131-139
- DOI: https://doi.org/10.1090/S0002-9947-1974-0344376-1
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Abstract:
It is the purpose of this paper to clarify the relationship between the square-integrable irreducible representations of a 2nd countable unimodular locally compact group G and a closed normal subgroup N using the Mackey theory relating the dual spaces $\hat G$ and $\hat N$.References
- Larry Baggett, A separable group having a discrete dual space is compact, J. Functional Analysis 10 (1972), 131â148. MR 0346090, DOI 10.1016/0022-1236(72)90045-6
- Jacques Dixmier, Les $C^{\ast }$-algĂšbres et leurs reprĂ©sentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Ăditeur-Imprimeur, Paris, 1964 (French). MR 0171173
- Edward G. Effros and Frank Hahn, Locally compact transformation groups and $C^{\ast }$- algebras, Memoirs of the American Mathematical Society, No. 75, American Mathematical Society, Providence, R.I., 1967. MR 0227310
- Frederick Greenleaf and Martin Moskowitz, Cyclic vectors for representations of locally compact groups, Math. Ann. 190 (1971), 265â288. MR 297926, DOI 10.1007/BF01431155
- G. Hochschild, The structure of Lie groups, Holden-Day, Inc., San Francisco-London-Amsterdam, 1965. MR 0207883
- A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57â110 (Russian). MR 0142001
- George W. Mackey, Induced representations of locally compact groups. II. The Frobenius reciprocity theorem, Ann. of Math. (2) 58 (1953), 193â221. MR 56611, DOI 10.2307/1969786 â, The theory of group representations, Lecture Notes (Summer, 1955), Dept. of Math., Univ. of Chicago, Chicago, Ill. MR 19, 117.
- Marc A. Rieffel, Square-integrable representations of Hilbert algebras, J. Functional Analysis 3 (1969), 265â300. MR 0244780, DOI 10.1016/0022-1236(69)90043-3 A. Weil, LâintĂ©gration dans les groupes topologiques et ses applications, Hermann, Paris, 1940.
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 194 (1974), 131-139
- MSC: Primary 22D10
- DOI: https://doi.org/10.1090/S0002-9947-1974-0344376-1
- MathSciNet review: 0344376