Geometry of biinvariant subsets of complex semisimple Lie groups

Gregor Fels; Laura Geatti

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)

  • Volume: 26, Issue: 2, page 329-356
  • ISSN: 0391-173X

How to cite

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Fels, Gregor, and Geatti, Laura. "Geometry of biinvariant subsets of complex semisimple Lie groups." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 26.2 (1998): 329-356. <http://eudml.org/doc/84331>.

@article{Fels1998,
author = {Fels, Gregor, Geatti, Laura},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {CR-geometry; representations of groups; generic orbits},
language = {eng},
number = {2},
pages = {329-356},
publisher = {Scuola normale superiore},
title = {Geometry of biinvariant subsets of complex semisimple Lie groups},
url = {http://eudml.org/doc/84331},
volume = {26},
year = {1998},
}

TY - JOUR
AU - Fels, Gregor
AU - Geatti, Laura
TI - Geometry of biinvariant subsets of complex semisimple Lie groups
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1998
PB - Scuola normale superiore
VL - 26
IS - 2
SP - 329
EP - 356
LA - eng
KW - CR-geometry; representations of groups; generic orbits
UR - http://eudml.org/doc/84331
ER -

References

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  1. [Bo] A. Boggess, CR-Manifolds and Tangential Cauchy-Riemann Complex, Studies in Advanced Math., C.R.C. Press, 1991. Zbl0760.32001MR1211412
  2. [Br] R. Bremigan, Invariant analytic domains in complex semisimple groups, Transformation Groups1 (1996), 279-305. Zbl0867.22004MR1424446
  3. [FH] G. Fels - A.T. Huckleberry, A Characterisation of K-Invariant Stein Domains in Symmetric Embeddings, Complex Analysis and Geometry, Plenum Press, New York, 1993, 223-234. Zbl0790.32030MR1211883
  4. [Gr] S.J. Greenfield, Cauchy-Riemann equations in several complex variables, Ann. Scuola Norm. Sup. Pisa22 (1968), 257-314. Zbl0159.37502MR237816
  5. [GG] I.M. Gelfand - S.G. Gindikin, Complex manifolds whose skeletons are semisimple real Lie groups, and analytic discrete series of representations, Functional Anal. Appl. 7-4 (1977), 19-27. Zbl0444.22006MR492076
  6. [HN] J. Hilgert - K.H. Neeb, Lie Semigroups and their Applications, Lecture Notes in Math. 1552, Springer Verlag, 1993. Zbl0807.22001MR1317811
  7. [Hu] J.E. Humphreys, Conjugacy Classes in Semisimple Algebraic Groups, Mathematical Surveys and Monographs, Vol. 43, AMS, Providence, Rhole Island, 1995. Zbl0834.20048MR1343976
  8. [Las] M. Lassalle, Séries de Laurent des fonctions holomorphes dans la complexification d'une espace symétrique compact, Ann. Sci. École Norm. Sup.4 (1973), 267-290. Zbl0452.43011
  9. [L1] J.J. Loeb, Plurisubharmonicité et convexité sur les groupes reductifs complexes, Pub. IRMA-Lille 2 VIII (1986), 1-12. 
  10. [L2] J.J. Loeb, Action d'une forme réelle d'un groupe de Lie complexe sur les fonctions plurisubharmoniques, Ann. Inst. Fourier35 (1985), 59-97. Zbl0563.32013MR812319
  11. [MO] T. Matsuki - T. Oshima, Orbits of affine symmetric spaces under the action of the isotropy groups, J. Math. Soc. Japan32 (1980), 399-414. Zbl0451.53039MR567427
  12. [N1] K.H. Neeb, Invariant convex sets and functions in Lie Algebras, Semigroups Forum53 (1996), 305-349. Zbl0873.17009MR1400650
  13. [N2] K.H. Neeb, On the Complex and Convex Geometry of Ol'shanskiĭ semigroups, preprint 10, Institut Mittag-Leffler, 1995/ 96. MR1614894
  14. [O1] G I. OL'SHANSKIĭ, Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series, Functional Anal. Appl.15 (1982), 275-285. Zbl0503.22011MR639200
  15. [O2] G.I. Ol'shanski, Complex Lie semigroups, Hardy spaces and the program of Gelfand Gindikin, Differential Geom. Appl.1 (1982), 235-246. Zbl0789.22011MR1244445
  16. [Ra] P.K. Rashevskij, On the connectedness of the fixed point set of an automorphism of a Lie group, Funct. Anal. Appl.6 (1973), 341-342. Zbl0285.54036
  17. [St] R.J. Stanton, Analytic extension of the holomorphic discrete series, Amer. J. Math.108 (1986), 1411-1424. Zbl0626.43008MR868896
  18. [Su] M. Sugiura, Conjugate classes of Cartan subalgebras in real semisimple Lie Algebras, J. Math. Soc. Japan11 (1959), 374-434. Zbl0204.04201MR146305
  19. [Tu] A.E. Tumanov, The geometry of CR-Manifolds, Encyclopaedia of Mathematical Sciences, Vol. 9, Springer Verlag, 1989, 201-221. Zbl0658.32007

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