Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

On Weyl group equivariant maps

Author(s): Adam Korányi; Róbert Szoke
Journal: Proc. Amer. Math. Soc. 134 (2006), 3449-3456.
MSC (2000): Primary 20F55, 22E46, 53C35
Posted: June 27, 2006
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

Abstract: We prove an equivariant analogue of Chevalley's isomorphism theorem for polynomial, $ C^{\infty }$ or $ C^{\omega }$ maps.


References:

[B]
Bourbaki, N., Groupes et algèbres de Lie, Chapitres 4, 5 et 6, Hermann, Paris 1968. MR 0240238 (39:1590)

[C]
Chevalley, C., Invariants of finite groups generated by reflections, Amer. J. Math 77 (1955), 778-782. MR 0072877 (17:345d)

[D-Sz]
Dancer, A. and Szoke, R., Symmetric spaces, adapted complex structures and hyperkähler structures, Quart. J. Math. Oxford 48 (1997), 27-38. MR 1439696 (98e:53083)

[D]
Dadok, J., On the $ C^{\infty }$ Chevalley's theorem, Adv. in Math 44 (1982), 121-131. MR 0658537 (83m:53073)

[H1]
Helgason, S., Differential Geometry, Lie Groups, and Symmetric Spaces, AMS, 2001. MR 1834454 (2002b:53081)

[H2]
-, Groups and Geometric Analysis, AMS, 2000. MR 1790156 (2001h:22001)

[HC]
Harish-Chandra, Spherical functions on a semisimple Lie group. I., Amer. J. Math 80 (1958), 241-310. MR 0094407 (20:925)

[L]
Luna, D., Fonctions différentiables invariantes sous l'opération d'un groupe réductif, Ann. Inst. Fourier, Grenoble 26 (1976), 33-49. MR 0423398 (54:11377)

[M1]
Michor, P., Basic differential forms for actions of Lie groups, Proc. AMS 124 (1996), 1633-1642. MR 1307550 (96g:57041)

[M2]
-, Basic differential forms for actions of Lie groups. II, Proc. AMS 125 (1997), 2175-2177. MR 1401750 (97k:57046)

[Sch]
Schwarz, G. W., Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975), 63-68. MR 0370643 (51:6870)

[S]
Solomon, L., Invariants of finite reflection groups, Nagoya Math. J. 22 (1963), 57-64. MR 0154929 (27:4872)


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20F55, 22E46, 53C35

Retrieve articles in all Journals with MSC (2000): 20F55, 22E46, 53C35


Additional Information:

Adam Korányi
Affiliation: Department of Mathematics, Lehman College, The City University of New York, Bedford Park Boulevard West, Bronx, New York 10468
Email: adam.koranyi@lehman.cuny.edu

Róbert Szoke
Affiliation: Department of Analysis, Eötvös University, Pázmány Péter sétány 1/c, Budapest, 1117 Hungary
Email: rszoke@cs.elte.hu

DOI: 10.1090/S0002-9939-06-08589-3
PII: S 0002-9939(06)08589-3
Keywords: Symmetric spaces, equivariant maps, reflection groups
Received by editor(s): July 24, 2004
Received by editor(s) in revised form: July 4, 2005
Posted: June 27, 2006
Additional Notes: The first author was partially supported by the National Science Foundation of the USA and by a PSC-CUNY grant.
The second author's research was partially supported by the Hungarian Science Foundation (OTKA) under grant T49449.
Communicated by: Dan M. Barbasch
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google