Induced representations of nonlocally compact groups
Matematičeskie zametki, Tome 57 (1995) no. 3, pp. 350-358.

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P. Gibilisco. Induced representations of nonlocally compact groups. Matematičeskie zametki, Tome 57 (1995) no. 3, pp. 350-358. http://geodesic.mathdoc.fr/item/MZM_1995_57_3_a3/

[1] Loomis L. H., “Positive definite functions and induced representations”, Duke Math., 27 (1960), 569–580 | DOI | MR

[2] Mackey G. W., “Imprimitivity for representations of locally compact groups, I”, Proc. Nat. Acad. Sci. U.S.A., 35 (1949), 537–545 | DOI | MR | Zbl

[3] Mackey G. W., “Unitary representations of group extensions, I”, Acta Math., 99 (1958), 265–311 | DOI | MR | Zbl

[4] Loll R., “A new quantum representation for the canonical gravity and $\operatorname {SU}(2)$ Yang–Mills theory”, Nucl. Phys. B, 350 (1991), 831–860 | DOI | MR

[5] Blattner R. J., “Positive definite measures”, Proc. Amer. Math. Soc., 14 (1963), 423–428 | DOI | MR | Zbl

[6] Jorgensen P. E. T., Operators and representation theory, North-Holland, Amsterdam, 1988

[7] Ørsted B., “Induced representation and a new proof of the imprimitivity theorem”, J. Funct. Anal., 31 (1979), 355–359 | DOI | MR

[8] Fell J. M. G., An extension of Mackeys method to Banach $*$-algebraic bundles, Memoirs Amer. Math. Soc., 90, 1969 | MR | Zbl

[9] Fell J. M. G., Doran R. S., Representations of $*$-algebras, locally compact groups, and Banach $*$-algebraic bundles, V. 1, 2, Academic Press, 1988 | Zbl

[10] Green P., “The local structure of twisted covariance algebras”, Acta Math., 140 (1978), 191–250 | DOI | MR | Zbl

[11] Mansfield K., “Induced representations of crossed products by coactions”, J. Funct. Anal., 97 (1991), 112–161 | DOI | MR | Zbl

[12] Rieffel M. A., “Induced representation of $C^*$-algebras”, Adv. in Math., 13 (1974), 176–257 | DOI | MR | Zbl

[13] Takesaki M., “Covariant representation of $C^*$-algebras and their locally compact automorphism groups”, Acta Math., 119 (1967), 273–303 | DOI | MR | Zbl

[14] Barut A. O., Rancka R., Theory of group representations and applications, World scientific, 1986 | Zbl

[15] Accardi L., “The Weyl–Schrödinger representation on curved space and Functional Integrals on the Connections”, Proceedings of the X Italian Relativity Conference, World Scientific (to appear)

[16] Accardi L., Gibilisco P., “The Schrödinger representation on Hilbert bundles”, Probabilistic Methods in Mathematical Physics (Siena, 1991), eds. Guerra F., Loffredo M. I., Marchioro C., World Scientific, 1992

[17] Borisov A. B., “The unitary representation of the Diff $R^N$ group”, J. Phys. A: Math. Gen., 12 (1979), 1625 | DOI | MR | Zbl

[18] Gibilisco P., Rappresentazioni indotte di gruppi di cammini e trasporti paralleli, Ph. d. Thesis (in Italian), Università degli studi di Roma “La Sapienza”, 1992

[19] Girardello L., Parravicini G., “Some remarks on the representations of infinite parameter groups and of the BMS group”, Group theoretical methods in physics, Proc. third Internat. Colloq., Centre Phys. Theor., Marseille, 1974

[20] Goldin G. A., Menikoff R., Sharp D. H., “Particle statistics from induced representation of a local current group”, J. Math. Phys., 21 (1980), 650 | DOI | MR | Zbl

[21] Goldin G. A., Menikoff R., Sharp D. H., “Induced representation of the group of diffeomorphisms”, J. Phys., 16 (1983), 1827–1833 | DOI | MR | Zbl

[22] Goldin G. A., Menikoff R., Sharp D. H., “Diffeomorphism Groups, Gauge Groups, and Quantum Theory”, Phys. Rev. Lett., 51:25 (1983) | DOI | MR

[23] Goldin G. A., Menikoff R., Sharp D. H., “Diffeomophism Groups and Quantized Vortex Filaments”, Phys. Rev. Lett., 58 (1987), 2162 | DOI | MR

[24] Goldin G. A., Sharp D. H., “Particle spin from representations of the diffeomorphism group”, Commun. Math. Phys., 92 (1983), 217–228 | DOI | MR | Zbl

[25] Isham C. J., “Topological and global aspects of quantum theory”, Relativity, groups and topology, V. II (Les Houches), eds. DeWitt B. S., Stora R., North Holland, Amsterdam, 1983

[26] Isham C. J., Kaukas A. C., “A group theoretical approach to the canonical quantization of gravity. I: Construction of the canonical group”, Class. Quantum Grav., 1 (1984), 621–632 | DOI | MR | Zbl

[27] Isham C. J., Kaukas A. C., “A group theoretical approach to the canonical quantization of gravity. II: Unitary representations of the canonical group”, Class. Quantum Grav., 1 (1984), 633–650 | DOI | MR | Zbl

[28] Marion J., Induction-unitarization process for some non-locally compact topological groups, Universität Bielefeld Preprint BiBoS, No 471, 1991

[29] Mensky M. B., Method of induced representations: Space-time and concept of particle, in Russian, Nauka, Moscow, 1976

[30] Mensky M. B., “The path group and the interaction of quantum string”, Sov. Phys. JETP, 63 (2) (1986)

[31] Dixmier J., Von Neumann Algebras, North-Holland Math. Lib., 27, 1981 | MR | Zbl

[32] Gibilisco P., “The imprimitivity theorem for a class of non-locally compact groups”, Proceedings of the X Italian Relativity Conference, World Scientific (to appear)

[33] Mackey G. W., Unitary representations in Physics, Probability and Number Theory, Benjamin-Cummings Publ. Comp., 1978 | Zbl

[34] Wallach N. R., Harmonic analysis on homogeneous space, Marcel Dekker, New York, 1973 | Zbl