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Holomorphic and abstract inducing

Published online by Cambridge University Press:  24 October 2008

K. C. Hannabuss
K. C. Hannabuss
Affiliation:
Balliol College, Oxford OX1 3BJ
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Abstract

A method of constructing projective representations of separable locally compact groups in reproducing kernel Hilbert spaces is presented, based on the generalized inducing process of Rieffel and Fell. Examples show that the method can be used to construct some well-known holomorphically induced representations. Some representations on cohomology spaces are also described.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 3 , November 1984 , pp. 453 - 468
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Aronszajn, J. N. A.. A theory of reproducing kernels. Trans. Amer. Math. Soc. 68 (1950) 337–404.CrossRefGoogle Scholar
[2]Bargmann, V.. On a Hilbert space of analytic functions and an associated integral transform. Commun. Pure Appl. Math. 14 (1961), 187–214.Google Scholar
[3]Bargmann, V.. On the representations of the rotation group. Rev. Mod. Phys. 34 (1962), 829–845.Google Scholar
[4]Carey, A. L.. Group representations in reproducing kernel hilbert spaces. Reports Math., Phys. 14 (1978), 247–259.CrossRefGoogle Scholar
[5]Dixmier, J.. Les C*-algébres et leurs représentations, Gauthier-Villars, Paris, 1969; English translation, C *-algebras (North-Holland, 1977).Google Scholar
[6]Fell, J. M. G.. Induced Representations and Banach*-algebra Bundles Lecture Notes in Math. vol. 582 (Springer-Verlag, 1978).Google Scholar
[7]Hannabuss, K. C.. Characters and contact transformations. Math. Proc. Cambridge. Philos. Soc. 90 (1981), 465–476.CrossRefGoogle Scholar
[8]Harish-Chandra, . Discrete series for semi-simple Lie groups. II. Acta Math. 116 (1966), 1–111.Google Scholar
[9]Harish-Chandra, . Harmonic analysis on semi-simple Lie groups. Bull. Amer. Math. Soc. 76 (1970), 529–551.CrossRefGoogle Scholar
[10]Howe, R.. θ-series and invariant theory. Proc. Symp. Pure Math. Amer. Math. Soc. 33 (1979), 275–285.CrossRefGoogle Scholar
[11]Kirillov, A. A.. Elementy teorii predstavlenii, Nauka, Moscow, 1972; English trans. Elements of the theory of representations (Springer-Verlag, 1976).Google Scholar
[12]Krein, M. G.. Hermitian positive kernels. Amer. Math. Soc. Translations (2) 34 (1963), 69–103 and 109–164.Google Scholar
[13]Langlands, R. P.. The dimension of spaces of automorphic forms. Amer. J. Math. 85 (1963) 99–125.CrossRefGoogle Scholar
[14]Mackey, G. W.. Induced representations of locally compact groups. II. Ann. of Math. 58 (1953), 193–221.CrossRefGoogle Scholar
[15]Mackey, G. W.. On the analogy between semi-simple Lie groups and certain semi-direct product groups and their representations. In Lie Groups, ed. Gel'fand, I. M. (Hilger, 1974).Google Scholar
[16]Rieffel, M. A.. Induced representations of C*-algebras. Adv. in Math. 13 (1974), 176–257.Google Scholar
[17]Schwartz, L.. Théorie des Distributions (Hermann, 1966).Google Scholar
[18]Segal, I. E.. Foundations of the theory of dynamical systems of infinitely many degrees of freedom. I. Mat. Fys. Medd. Danske Vid. Selsk. 31 (1959), 1–39.Google Scholar