On the infinitesimal kernel of irreducible representations of nilpotent Lie groups

Niels Vigand Pedersen

Bulletin de la Société Mathématique de France (1984)

  • Volume: 112, page 423-467
  • ISSN: 0037-9484

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Pedersen, Niels Vigand. "On the infinitesimal kernel of irreducible representations of nilpotent Lie groups." Bulletin de la Société Mathématique de France 112 (1984): 423-467. <http://eudml.org/doc/87472>.

@article{Pedersen1984,
author = {Pedersen, Niels Vigand},
journal = {Bulletin de la Société Mathématique de France},
keywords = {infinitesimal kernel; parametrization by polynomial functions; simply connected nilpotent Lie group; enveloping algebra; irreducible representation; coadjoint orbit; symmetrization map},
language = {eng},
pages = {423-467},
publisher = {Société mathématique de France},
title = {On the infinitesimal kernel of irreducible representations of nilpotent Lie groups},
url = {http://eudml.org/doc/87472},
volume = {112},
year = {1984},
}

TY - JOUR
AU - Pedersen, Niels Vigand
TI - On the infinitesimal kernel of irreducible representations of nilpotent Lie groups
JO - Bulletin de la Société Mathématique de France
PY - 1984
PB - Société mathématique de France
VL - 112
SP - 423
EP - 467
LA - eng
KW - infinitesimal kernel; parametrization by polynomial functions; simply connected nilpotent Lie group; enveloping algebra; irreducible representation; coadjoint orbit; symmetrization map
UR - http://eudml.org/doc/87472
ER -

References

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  1. [1] BROWN (I. D.). — Dual topology of a nilpotent Lie group, Ann. scient. Ec. Norm. Sup., T. 6, No. 4, 1973, pp. 407-411. Zbl0284.57026MR50 #4813
  2. [2] DIXMIER (J.). — Traces sur les C*-algèbres, Ann. Inst. Fourier (Grenoble), Vol. 13, 1963, pp. 219-262. Zbl0118.11303MR26 #6807
  3. [3] DIXMIER (J.). — Représentation irréductibles des algèbres de Lie nilpotents, An. Acad. Brasil Ci., Vol. 35, 1963, pp. 491-519. Zbl0143.05302MR32 #165
  4. [4] DIXMIER (J.). — Sur le dual d'un groupe de Lie nilpotent, Bull. Sc. Math., Vol. 90, 1966, pp. 113-118. Zbl0144.26606MR35 #298
  5. [5] DIXMIER (J.). — Algèbres enveloppantes, Gauthier-Villars, Paris, 1974. Zbl0308.17007MR58 #16803a
  6. [6] GODFREY (C.). — Ideals of coadjoint orbits of nilpotent Lie algebras, Trans. Amer. Math. Soc., Vol. 233, 1977, pp. 295-307. Zbl0316.17006MR56 #5672
  7. [7] KIRILLOV (A. A.). — Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk. Vol. 17, 1962, pp. 57-110. Zbl0106.25001MR25 #5396
  8. [8] PEDERSEN (N. V.). — On the characters of exponential solvable Lie groups, Ann. scient. Écol. Norm. Sup., T. 17, 1984, pp. 1-29. Zbl0578.22007MR85k:22022
  9. [9] PUKANSZKY (L.). — Leçons sur les représentations des groupes, Dunod, Paris, 1967. Zbl0152.01201MR36 #311
  10. [10] PUKANSZKY (L.). — On the characters and the Plancherel formula of nilpotent groups, J. Funct. Anal., Vol. 1, 1967, pp. 255-280. Zbl0165.48603MR37 #4236
  11. [11] PUKANSZKY (L.). — Unitary representations of solvable Lie groups, Ann. scient. Ecol. Norm. Sup., T. 4, No. 4, 1971, pp. 457-608. Zbl0238.22010MR55 #12866

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