Type I criteria and the Plancherel formula for Lie groups with co-compact radical

Ronald L. Lipsman

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1982)

  • Volume: 9, Issue: 2, page 263-285
  • ISSN: 0391-173X

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Lipsman, Ronald L.. "Type I criteria and the Plancherel formula for Lie groups with co-compact radical." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 9.2 (1982): 263-285. <http://eudml.org/doc/83882>.

@article{Lipsman1982,
author = {Lipsman, Ronald L.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {orbit method; type I; Plancherel formula; reductive Lie groups; polarizations; irreducible unitary representations; holomorphic induction},
language = {eng},
number = {2},
pages = {263-285},
publisher = {Scuola normale superiore},
title = {Type I criteria and the Plancherel formula for Lie groups with co-compact radical},
url = {http://eudml.org/doc/83882},
volume = {9},
year = {1982},
}

TY - JOUR
AU - Lipsman, Ronald L.
TI - Type I criteria and the Plancherel formula for Lie groups with co-compact radical
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1982
PB - Scuola normale superiore
VL - 9
IS - 2
SP - 263
EP - 285
LA - eng
KW - orbit method; type I; Plancherel formula; reductive Lie groups; polarizations; irreducible unitary representations; holomorphic induction
UR - http://eudml.org/doc/83882
ER -

References

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  2. [2] J. Brezin, Unitary representation theory for solvable Lie groups, Mem. Amer. Math. Soc., 79 (1968). Zbl0157.36603MR227311
  3. [3] J. Charbonnel, La formule de Plancherel pour un groupe de Lie résoluble connexe, Thèse 3ième cycle, U. ParisVII (1976). (See also Lectures Notes in Math., 587 (1977), pp. 32-76.) Zbl0365.22009MR486309
  4. [4] J. Charbonnel - M. Khalgui, Polarisations pour un certain type de groupes de Lie, C.R. Acad. Sci., 287 (1978), pp. 915-917. Zbl0394.22013MR520767
  5. [5] M. Duflo, Sur les extensions des representations irreductibles des groupes de Lie nilpotents, Ann. Sci. École Norm. Sup., 5 (1972), pp. 71-120. Zbl0241.22030MR302823
  6. [6] M. Duflo, Construction de représentations unitaires d'un groupe de Lie, Cortona (1980), preprint. MR626830
  7. [7] M. Duflo - C. Moore, On the regular representation of a non-unimodular locally compact group, J. Functional Analysis, 21 (1976), pp. 209-243. Zbl0317.43013MR393335
  8. [8] Harish-Chandra, Harmonic analysis on real reductive groups - I, J. Functional Analysis, 19 (1975), pp. 104-204. Zbl0315.43002MR399356
  9. [9] R. Kallman, Certain topological groups are type I, Bull. Amer. Math. Soc., 76 (1970), pp. 404-406. Zbl0192.48202MR255725
  10. [10] R. Kallman, Certain topological groups are type I. Part 11, Advances in Math., 10 (1973), pp. 221-255. Zbl0255.22012MR338256
  11. [11] M. Khalgui, Sur les caracteres des groupes de Lie à radical co-compact, preprint. 
  12. [12] A. Kleppner - R. Lipsman, The Plancherel formula for group extensions, Ann. Sci. École Norm. Sup., 5 (1972), pp. 459-516. Zbl0239.43003MR342641
  13. [13] A. Kleppner - R. Lipsman, The Plancherel formula for group extensions - II, Ann. Sci. École Norm. Sup., 6 (1973), pp. 103-132. Zbl0258.43001
  14. [14] R. Lipsman, Characters of Lie groups - II: Real polarizations and the orbital-integral character formula, J. Analyse Math., 31 (1977), pp. 257-286. Zbl0351.22009MR579006
  15. [15] R. Lipsman, Orbit theory and harmonic analysis on Lie groups with co-compact nilradical, J. Math. Pures Appl., 59 (1980), pp. 337-374. Zbl0421.22005MR604474
  16. [16] R. Lipsman, Orbit theory and representations of Lie groups with co-compact radical, J. Math. Pures Appl., 60 (1981), to appear. Zbl0494.22011MR664340
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  18. [18] L. Pukanszky, Characters of connected Lie groups, Acta Math., 133 (1974), pp. 81-137. Zbl0323.22011MR409728
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  21. [21] M. Vergne, A Plancherel formula without group representations, preprint. MR733319

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