Induced representations of completely solvable Lie groups

Ronald L. Lipsman

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1990)

  • Volume: 17, Issue: 1, page 127-164
  • ISSN: 0391-173X

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Lipsman, Ronald L.. "Induced representations of completely solvable Lie groups." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 17.1 (1990): 127-164. <http://eudml.org/doc/84066>.

@article{Lipsman1990,
author = {Lipsman, Ronald L.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {induced representations; completely solvable Lie groups; orbit method; Lie algebra; connected subgroup; irreducible unitary representation; unitary dual; coadjoint orbits; decomposition formula},
language = {eng},
number = {1},
pages = {127-164},
publisher = {Scuola normale superiore},
title = {Induced representations of completely solvable Lie groups},
url = {http://eudml.org/doc/84066},
volume = {17},
year = {1990},
}

TY - JOUR
AU - Lipsman, Ronald L.
TI - Induced representations of completely solvable Lie groups
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1990
PB - Scuola normale superiore
VL - 17
IS - 1
SP - 127
EP - 164
LA - eng
KW - induced representations; completely solvable Lie groups; orbit method; Lie algebra; connected subgroup; irreducible unitary representation; unitary dual; coadjoint orbits; decomposition formula
UR - http://eudml.org/doc/84066
ER -

References

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  2. [2] P. Bernat, et al., Représentations des groupes de Lie résolubles, Dunod, Paris, 1972. Zbl0248.22012MR444836
  3. [3] I. Butsyatskaya, Representations of exponential Lie groups, Functional Anal. Appl., 7 (1973), 151-152. Zbl0286.22013MR325855
  4. [4] L. Corwin - F. Greenleaf - G. Grelaud, Direct integral decompositions and multiplicities for induced representations of nilpotent Lie groups, Trans. Amer. Math. Soc., 304 (1987), 549-583. Zbl0629.22005MR911085
  5. [5] L. Corwin - F. Greenleaf, Complex algebraic geometry and calculation of multiplicities for induced representations of nilpotent Lie groups, Trans. Amer. Math. Soc., 305 (1988), 601-622. Zbl0651.22004MR924771
  6. [6] A. Kirillov, Unitary representations of nilpotent Lie groups, Russian Math. Surveys, 17 (1962), 53-104. Zbl0106.25001MR142001
  7. [7] A. Kleppner - R. Lipsman, The Plancherel formula for group extensions I, Ann. Sci. Ecole Norm. Sup., 5 (1972), 459-516. Zbl0239.43003MR342641
  8. [8] R. Lipsman, Characters of Lie groups II, J. Analyse Math., 31 (1977), 257-286. Zbl0351.22009MR579006
  9. [9] R. Lipsman, Orbital parameters for induced and restricted representations, Trans. Amer. Math. Soc., 313 (1989), 433-473. Zbl0683.22009MR930083
  10. [10] R. Lipsman, Harmonic analysis on exponential solvable homogeneous spaces: The algebraic or symmetric cases, Pacific J. Math., 140 (1989), 117-147. Zbl0645.43010MR1019070
  11. [11] G. Mackey, Unitary representations of group extensions, Acta Math., 99 (1958), 265-311. Zbl0082.11301MR98328
  12. [12] L. Pukanszky, Unitary representations of Lie groups with co-compact radical and applications, Trans Amer. Math. Soc., 236 (1978), 1-49. Zbl0389.22009MR486313
  13. [13] O. Takenouchi, Sur la facteur représentation d'une groupe de Lie résoluble de type (E), Math. J. Okayama Univ., 7 (1957), 151-161. Zbl0080.02302MR97464

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