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Induced and produced representations of Lie algebras
Author:
Robert J. Blattner
Journal:
Trans. Amer. Math. Soc. 144 (1969), 457-474
MSC:
Primary 17B15
MathSciNet review:
0308223
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References |
Similar Articles |
Additional Information
- [1]
Robert
J. Blattner, Positive definite measures,
Proc. Amer. Math. Soc. 14 (1963), 423–428. MR 0147580
(26 #5095), http://dx.doi.org/10.1090/S0002-9939-1963-0147580-9
- [2]
J.
Dixmier, Représentations irréductibles des
algèbres de Lie nilpotentes, An. Acad. Brasil. Ci.
35 (1963), 491–519 (French). MR 0182682
(32 #165)
- [2a]
J.
Dixmier, Représentations irréductibles des
algèbres de Lie résolubles, J. Math. Pures Appl. (9)
45 (1966), 1–66 (French). MR 0200393
(34 #288)
- [3]
Victor
W. Guillemin and Shlomo
Sternberg, An algebraic model of transitive
differential geometry, Bull. Amer. Math.
Soc. 70 (1964),
16–47. MR
0170295 (30 #533), http://dx.doi.org/10.1090/S0002-9904-1964-11019-3
- [3a]
Victor W. Guillemin, D. C. Spencer and Shlomo Sternberg, Representation theory of transitive Lie algebras. 1: The Mackey imprimitivity theorem and its generalization, (unpublished).
- [4]
Harish-Chandra,
On some applications of the universal
enveloping algebra of a semisimple Lie algebra, Trans. Amer. Math. Soc. 70 (1951), 28–96. MR 0044515
(13,428c), http://dx.doi.org/10.1090/S0002-9947-1951-0044515-0
- [5]
-, Representations of a semi-simple Lie group on a Banach space. I, Trans. Amer. Math. Soc. 75 (1953), 185-243.
- [6]
D.
G. Higman, Induced and produced modules, Canad. J. Math.
7 (1955), 490–508. MR 0087671
(19,390b)
- [7]
George
W. Mackey, Imprimitivity for representations of locally compact
groups. I, Proc. Nat. Acad. Sci. U. S. A. 35 (1949),
537–545. MR 0031489
(11,158b)
- [8]
George
W. Mackey, Unitary representations of group extensions. I,
Acta Math. 99 (1958), 265–311. MR 0098328
(20 #4789)
- [9]
D.
S. Rim, Deformation of transitive Lie algebras, Ann. of Math.
(2) 83 (1966), 339–357. MR 0199315
(33 #7463)
- [10]
Séminaire ``Sophus Lie'' 1955-1956, Secrétariat mathématique, Paris, 1957.
- [11]
I.
M. Singer and Shlomo
Sternberg, The infinite groups of Lie and Cartan. I. The transitive
groups, J. Analyse Math. 15 (1965), 1–114. MR 0217822
(36 #911)
- [12]
Nolan
R. Wallach, Induced representations of Lie
algebras and a theorem of Borel-Weil., Trans.
Amer. Math. Soc. 136 (1969), 181–187. MR 0233937
(38 #2258), http://dx.doi.org/10.1090/S0002-9947-1969-0233937-4
- [1]
- Robert J. Blattner, Positive definite measures, Proc. Amer. Math. Soc. 14 (1963), 423-428. MR 0147580 (26:5095)
- [2]
- J. Dixmier, Représentations irréductibles des algèbres de Lie nilpotentes, An. Acad. Brasil. Ci. 35 (1963), 491-519. MR 0182682 (32:165)
- [2a]
- J. Dixmier, Représentations irréductibles des algèbres de Lie résolubles, J. Math. Pures Appl. 45 (1966), 1-66. MR 0200393 (34:288)
- [3]
- Victor W. Guillemin and Shlomo Sternberg, An algebraic model of transitive differential geometry, Bull. Amer. Math. Soc. 70 (1964), 16-47. MR 0170295 (30:533)
- [3a]
- Victor W. Guillemin, D. C. Spencer and Shlomo Sternberg, Representation theory of transitive Lie algebras. 1: The Mackey imprimitivity theorem and its generalization, (unpublished).
- [4]
- Harish-Chandra, On some applications of the universal enveloping algebra of a semi-simple Lie algebra, Trans. Amer. Math. Soc. 70 (1951), 28-96. MR 0044515 (13:428c)
- [5]
- -, Representations of a semi-simple Lie group on a Banach space. I, Trans. Amer. Math. Soc. 75 (1953), 185-243.
- [6]
- D. G. Higman, Induced and produced modules, Canad. J. Math. 7 (1955), 490-508. MR 0087671 (19:390b)
- [7]
- G. W. Mackey, Imprimitivity for representations of locally compact groups. I, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 537-545. MR 0031489 (11:158b)
- [8]
- -, Unitary representations of group extensions. I, Acta Math. 99 (1958), 265-311. MR 0098328 (20:4789)
- [9]
- D. S. Rim, Deformations of transitive Lie algebras, Ann. of Math. (2) 83 (1966), 339-357. MR 0199315 (33:7463)
- [10]
- Séminaire ``Sophus Lie'' 1955-1956, Secrétariat mathématique, Paris, 1957.
- [11]
- I. M. Singer and Shlomo Sternberg, The infinite groups of Lie and Cartan. I: The transitive groups, J. Analyse Math. 15 (1965), 1-114. MR 0217822 (36:911)
- [12]
- Nolan R. Wallach, Induced representations of Lie algebras and a theorem of Borel-Weil, Trans. Amer. Math. Soc. 136 (1969), 181-187. MR 0233937 (38:2258)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1969-0308223-4
PII:
S 0002-9947(1969)0308223-4
Article copyright:
© Copyright 1969 American Mathematical Society
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