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Induced representations of nonlocally compact groups

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References

  1. L. H. Loomis, “Positive definite functions and induced representations,”Duke Math. J.,27, 569–580 (1960).

    Article  MATH  MathSciNet  Google Scholar 

  2. G. W. Mackey, “Imprimitivity for representations of locally compact groups. I,”Proc. Natl. Acad. Sci. USA,35, 537–545 (1949).

    MATH  MathSciNet  Google Scholar 

  3. G. W. Mackey, “Unitary representations of group extensions. I,”Acta Math.,99, 265–311 (1958).

    MATH  MathSciNet  Google Scholar 

  4. R. Loll, “A new quantum representation for the canonical gravity andSU(2) Yang-Mills theory,”Nucl. Phys. B,350, 831–860 (1991).

    Article  MathSciNet  Google Scholar 

  5. R. J. Blattner, “Positive definite measures,”Proc. Am. Math. Soc.,14, 423–428 (1963).

    MATH  MathSciNet  Google Scholar 

  6. P. E. T. Jorgensen,Operators and Representation Theory, North-Holland, Amsterdam (1988).

    Google Scholar 

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

    MathSciNet  Google Scholar 

  8. J. M. G. Fell, “An extension of Mackeys method to Banach *-algebraic bundles,”Memoirs Am. Math. Soc.,90 (1969).

  9. J. M. G. Fell and R. S. Doran,Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles. Vols. 1, 2, Academic Press (1988).

  10. P. Green, “The local structure of twisted covariance algebras,”Acta Math.,140, 191–250 (1978).

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  12. M. A. Rieffel, “Induced representation ofC *-algebras,”Adv. Math.,13, 176–257 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  13. Takesaki, “Covariant representation ofC *-algebras and their locally compact automorphism groups,”Acta Math.,119, 273–303 (1967).

    MATH  MathSciNet  Google Scholar 

  14. A. O. Barut and R. Racka,Theory of Group Representations and Applications, World Sci. (1986).

  15. L. Accardi, “The Weyl-Schrödinger representation on curved space and functional integrals on the connections,” in:Proceedings of the X Italian Relativity Conference, World Sci. (to appear).

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

  17. A. B. Borisov, “The unitary representation of the DiffR N group,”J. Phys. A: Math. Gen.,12, 1625 (1979).

    Article  MATH  MathSciNet  Google Scholar 

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

  19. L. Girardello and G. Parravicini, “Some remarks on the representations of infinite parameter groups and of the BMS group,” in:Group theoretical methods in physics (Proc. III Intern. Colloq., Centre Phys. Theor., Marseille) (1974).

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  22. G. A. Goldin, R. Menikoff, and D. H. Sharp, “Diffeomorphism groups, gauge groups, and quantum theory,”Phys. Rev. Lett.,51, 25 (1983).

    Article  MathSciNet  Google Scholar 

  23. G. A. Goldin, R. Menikoff, and D. H. Sharp, “Diffeomophism groups and quantized vortex filaments,”Phys. Rev. Lett.,58, 2162 (1987).

    MathSciNet  Google Scholar 

  24. G. A. Goldin and D. H. Sharp, “Particle spin from representations of the diffeomorphism group,”Comm. Math. Phys.,92, 217–228 (1983).

    Article  MathSciNet  Google Scholar 

  25. C. J. Isham, “Topological and global aspects of quantum theory,” in:Relativity, Groups and Topology. Vol II, Les Houches, 1983 (B. S. DeWitt and R. Stora, eds.), North Holland, Amsterdam (1984).

    Google Scholar 

  26. C. J. Isham and A. C. Kaukas, “A group theoretical approach to the canonical quantization of gravity. I. Construction of the canonical group,”Class. Quantum Grav.,1, 621–632 (1984).

    Google Scholar 

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

    Google Scholar 

  28. J. Marion, “Induction-unitarization process for some nonlocally compact topological groups,” Universität Bielefeld, Preprint BiBoS, No. 471 (1991).

  29. M. B. Menskii,Method of Induced Representations: Space-Time and Concept of Particle [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  30. M. B. Menskii, “The path group and the interaction of quantum string,”Sov. Phys. JETP,63, No. 2 (1986).

    Google Scholar 

  31. J. Dixmier, “Von Neumann Algebras,”North-Holland Math. Lib.,27 (1981).

  32. P. Gibilisco, “The imprimitivity theorem for a class of nonlocally compact groups,” in:Proceedings of the X Italian Relativity Conference, World Sci. (to appear).

  33. G. W. Mackey,Unitary Representations in Physics, Probability, and Number Theory, Benjamin-Cummings Publ. Co. (1978).

  34. N. R. Wallach,Harmonic Analysis on Homogeneous Space, Marcel Dekker, New York (1973).

    Google Scholar 

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Authors and Affiliations

  1. Centro Matematico V. Volterra, Dipartimento di Matematica, Università di Roma II, Via Orazio Raimondo, 00173, Roma, Italy

    P. Gibilisco

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Translated from Matematicheskie Zametki, Vol. 57, No. 3, pp. 350–358, March, 1995.

I express my deep gratitude to Professor Luigi Accardi for his assistance and encouragement.

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Gibilisco, P. Induced representations of nonlocally compact groups. Math Notes 57, 248–253 (1995). https://doi.org/10.1007/BF02303969

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