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Polarization and unitary representations of solvable Lie groups. Appendix by Calvin C. Moore. (English) Zbl 0233.22005

22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
22D10 Unitary representations of locally compact groups
22E70 Applications of Lie groups to the sciences; explicit representations
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[1] Auslander, L., Kostant, B.: Quantization and representations of solvable Lie groups. Bull. A.M.S.73, 692-695 (1967). · Zbl 0203.03302
[2] Auslander, L., Moore, C. C.: Unitary representations of solvable Lie groups. Memoirs A.M.S.62 (1966). · Zbl 0204.14202
[3] ?, Brezin, J.: Almost algebraic Lie algebras. J. of Algebra8, 295-313 (1968). · Zbl 0197.03002
[4] Bargmann, V.: On a Hilbert space of analytic functions and an associated integral transform I. Comm. Pure and Applied Math.14, 187-214 (1961). · Zbl 0107.09102
[5] Bernat, M. P.: Sur les representations unitaires des groupes de Lie resolubles. Ann. Sci. Ecole Norm. Sup.82, 37-99 (1965). · Zbl 0138.07302
[6] Brezin, J.: Unitary representation theory for solvable Lie groups. Memoirs A.M.S.79 (1968). · Zbl 0157.36603
[7] Kirillov, A. A.: Unitary representations of nilpotent Lie groups. Uspehi, Mat. Nauk.17, 57-110 (1962). · Zbl 0106.25001
[8] Kostant, B.: Quantization and unitary representations, p. 87-207, Lecture Notes in Mathematics.170. Berlin-Heidelberg-New York: Springer 1970. · Zbl 0223.53028
[9] Pukanszky, L.: On the theory of exponential groups. Trans. A.M.S.126, 487-507 (1967). · Zbl 0207.33605
[10] ?: Lecons sur les representations des groupes. Monographes Soc. Math. de France. Paris: Dunod 1967.
[11] Rosenlicht, M.: A remark on quotient spaces. Anais da Academic Brasileina de Ciencias35, 487-489 (1963). · Zbl 0123.13804
[12] Streater, R.F.: The representations of the oscillator group. Comm. Math. and Phys.4, 217-236 (1967). · Zbl 0155.32503
[13] Weil, A.: Varietes Kahleriennes, Actualites Scientific et Industrielle, 1267. Paris: Hermann 1958.
[14] Effros, E.: A decomposition theorem for representations of aC *-algebra. Trans. A.M.S.107, 83-106 (1963). · Zbl 0113.09602
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