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Induced and produced representations of Lie algebras.(English)Zbl 0295.17002


MSC:

17B15 Representations of Lie algebras and Lie superalgebras, analytic theory
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras

Cite

References:

[1]Robert J. Blattner, Positive definite measures, Proc. Amer. Math. Soc. 14 (1963), 423 – 428. ·Zbl 0135.36202
[2]J. Dixmier, Représentations irréductibles des algèbres de Lie nilpotentes, An. Acad. Brasil. Ci. 35 (1963), 491 – 519 (French). ·Zbl 0143.05302
[3]J. Dixmier, Représentations irréductibles des algèbres de Lie résolubles, J. Math. Pures Appl. (9) 45 (1966), 1 – 66 (French). ·Zbl 0136.30603
[4]Victor W. Guillemin and Shlomo Sternberg, An algebraic model of transitive differential geometry, Bull. Amer. Math. Soc. 70 (1964), 16 – 47. ·Zbl 0121.38801
[5]Victor W. Guillemin, D. C. Spencer and Shlomo Sternberg, Representation theory of transitive Lie algebras. 1: The Mackey imprimitivity theorem and its generalization, (unpublished).
[6]Harish-Chandra, On some applications of the universal enveloping algebra of a semisimple Lie algebra, Trans. Amer. Math. Soc. 70 (1951), 28 – 96. ·Zbl 0042.12701
[7]-, Representations of a semi-simple Lie group on a Banach space. I, Trans. Amer. Math. Soc. 75 (1953), 185-243. ·Zbl 0051.34002
[8]D. G. Higman, Induced and produced modules, Canad. J. Math. 7 (1955), 490 – 508. ·Zbl 0065.26001 ·doi:10.4153/CJM-1955-052-4
[9]George W. Mackey, Imprimitivity for representations of locally compact groups. I, Proc. Nat. Acad. Sci. U. S. A. 35 (1949), 537 – 545. ·Zbl 0035.06901
[10]George W. Mackey, Unitary representations of group extensions. I, Acta Math. 99 (1958), 265 – 311. ·Zbl 0082.11301 ·doi:10.1007/BF02392428
[11]D. S. Rim, Deformation of transitive Lie algebras, Ann. of Math. (2) 83 (1966), 339 – 357. ·Zbl 0136.43104 ·doi:10.2307/1970435
[12]Séminaire “Sophus Lie” 1955-1956, Secrétariat mathématique, Paris, 1957.
[13]I. M. Singer and Shlomo Sternberg, The infinite groups of Lie and Cartan. I. The transitive groups, J. Analyse Math. 15 (1965), 1 – 114. ·Zbl 0277.58008 ·doi:10.1007/BF02787690
[14]Nolan R. Wallach, Induced representations of Lie algebras and a theorem of Borel-Weil., Trans. Amer. Math. Soc. 136 (1969), 181 – 187. ·Zbl 0294.17005
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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