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
Full Text: DOI EuDML


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.