Duke Mathematical Journal

Representation theory of the Hilbert-Lie group $U(\mathfrak{H})_2$

Robert P. Boyer

Source: Duke Math. J. Volume 47, Number 2 (1980), 325-344.

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Primary Subjects: 22E65

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077314038
Mathematical Reviews number (MathSciNet): MR575900
Zentralblatt MATH identifier: 0462.22009
Digital Object Identifier: doi:10.1215/S0012-7094-80-04720-1

References

W. Arveson, Representations of unitary groups, preprint, 1977.
B. M. Baker, Free states of the gauge invariant canonical anticommutation relations, Trans. Amer. Math. Soc. 237 (1978), 35–61.
Mathematical Reviews (MathSciNet): MR80b:46081
Zentralblatt MATH: 0376.46041
Digital Object Identifier: doi:10.2307/1997609
V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Comm. Pure Appl. Math. 14 (1961), 187–214.
Mathematical Reviews (MathSciNet): MR28:486
Zentralblatt MATH: 0107.09102
Digital Object Identifier: doi:10.1002/cpa.3160140303
V. Bargmann, Remarks on a Hilbert space of analytic functions, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 199–204.
Mathematical Reviews (MathSciNet): MR24:A2845
Zentralblatt MATH: 0107.09103
Digital Object Identifier: doi:10.1073/pnas.48.2.199
A. Borel and A. Weil, Representations linéaires et espaces homogènes Kählerian des groups de Lie compacts, 1954, exposé J.-P. Serre, Séminaire Bourbaki, no. 100, Paris.
P. de la Harpe, Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space, Lecture Notes in Mathematics, vol. 285, Springer-Verlag, Berlin, 1972.
Mathematical Reviews (MathSciNet): MR57:16372
Zentralblatt MATH: 0256.22015
M. Goto, On algebraic homogeneous spaces, Amer. J. Math. 76 (1954), 811–818.
Mathematical Reviews (MathSciNet): MR16,568c
Zentralblatt MATH: 0056.39803
Digital Object Identifier: doi:10.2307/2372654
A. A. Kirillov, Representations of the infinite-dimensional unitary group, Dokl. Akad. Nauk. SSSR 212 (1973), 288–290.
Mathematical Reviews (MathSciNet): MR49:5239
Zentralblatt MATH: 0288.22020
H. H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Mathematics, vol. 463, Springer-Verlag, Berlin, 1975.
Mathematical Reviews (MathSciNet): MR57:1628
Zentralblatt MATH: 0306.28010
V. I. Kolomycev and Ju. S. Samoĭ lenko, Irreducible representations of inductive limits of groups, Ukrain. Mat. Ž. 29 (1977), no. 4, 526–531, 565.
Mathematical Reviews (MathSciNet): MR57:6282
G. I. Ol'shanskii, Unitary representations of the infinite-dimensional classical groups $U(p,\infty), SO_{0}(p,\infty), Sp(p,\infty)$ and the corresponding motion groups, Funct. Anal. and Appl. 12 (1978), 185–195.
Mathematical Reviews (MathSciNet): MR509382
I. E. Segal, Tensor algebras over Hilbert spaces. I, Trans. Amer. Math. Soc. 81 (1956), 106–134.
Mathematical Reviews (MathSciNet): MR17,880d
Zentralblatt MATH: 0070.34003
Digital Object Identifier: doi:10.2307/1992855
I. E. Segal, The structure of a class of representations of the unitary group on a Hilbert space, Proc. Amer. Math. Soc. 8 (1957), 197–203.
Mathematical Reviews (MathSciNet): MR18,812f
Zentralblatt MATH: 0078.29301
Digital Object Identifier: doi:10.2307/2032839
I. E. Segal, Mathematical characterization of the physical vacuum for a linear Bose-Einstein field. (Foundations of the dynamics of infinite systems. III), Illinois J. Math. 6 (1962), 500–523.
Mathematical Reviews (MathSciNet): MR26:1075
Zentralblatt MATH: 0106.42804
I. E. Segal, The complex-wave representation of the free boson field, Topics in functional analysis (essays dedicated to M. G. Kreĭn on the occasion of his 70th birthday), Advances in Math. Suppl. Studies, vol. 3, Academic Press, New York, 1978, pp. 321–343.
Mathematical Reviews (MathSciNet): MR82d:81069
Zentralblatt MATH: 0471.22024
D. Shale, Linear symmetries of free boson fields, Trans. Amer. Math. Soc. 103 (1962), 149–167.
Mathematical Reviews (MathSciNet): MR25:956
Zentralblatt MATH: 0171.46901
Digital Object Identifier: doi:10.2307/1993745
D. Shale, Invariant integration over the infinite dimensional orthogonal group and related spaces, Trans. Amer. Math. Soc. 124 (1966), 148–157.
Mathematical Reviews (MathSciNet): MR39:409
Zentralblatt MATH: 0179.18904
Digital Object Identifier: doi:10.2307/1994441
B. Simon, Notes on infinite determinants of Hilbert space operators, Advances in Math. 24 (1977), no. 3, 244–273.
Mathematical Reviews (MathSciNet): MR58:2401
Zentralblatt MATH: 0353.47008
E. Thoma, Die unzerlegbaren, positiv-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe, Math. Z. 85 (1964), 40–61.
Mathematical Reviews (MathSciNet): MR30:3382
Zentralblatt MATH: 0192.12402
Digital Object Identifier: doi:10.1007/BF01114877
M. Vergne, Groupe symplectique et seconde quantification, C. R. Acad. Sci. Paris Sér. A-B 285 (1977), no. 4, A191–A194.
Mathematical Reviews (MathSciNet): MR56:15848
Zentralblatt MATH: 0386.22014
D. Voiculescu, Représentations factorielles de type II1 de $U(\infty )$ , J. Math. Pures et Appl. (9) 55 (1976), no. 1, 1–20.
Mathematical Reviews (MathSciNet): MR56:541
Zentralblatt MATH: 0352.22014
S. Strătilă and D. Voiculescu, Representations of AF-algebras and of the group $U(\infty )$ , Lecture Notes in Mathematics, vol. 486, Springer-Verlag, Berlin, 1975.
Mathematical Reviews (MathSciNet): MR56:16391
Zentralblatt MATH: 0318.46069
Şerban Strătilă and Dan Voiculescu, On a class of KMS states for the unitary group ${\rm U}(\infty )$ , Math. Ann. 235 (1978), no. 1, 87–110.
Mathematical Reviews (MathSciNet): MR58:2327
Zentralblatt MATH: 0369.22012
Digital Object Identifier: doi:10.1007/BF01421594
N. Wallach, Harmonic analysis on homogeneous spaces, Marcel Dekker Inc., New York, 1973.
Mathematical Reviews (MathSciNet): MR58:16978
Zentralblatt MATH: 0265.22022
H. Weyl, The Classical Groups, Princeton University Press, 1946.
Mathematical Reviews (MathSciNet): MR1488158
D. P. Želobenko, Compact Lie groups and their representations, Translations of Mathematical Monographs, vol. 40, American Mathematical Society, Providence, R.I., 1973.
Mathematical Reviews (MathSciNet): MR57:12776b
Zentralblatt MATH: 0272.22006

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