On Weyl group equivariant maps
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- by Adam Korányi and Róbert Szőke PDF
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Abstract:
We prove an equivariant analogue of Chevalley’s isomorphism theorem for polynomial, $C^{\infty }$ or $C^{\omega }$ maps.References
- N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
- Claude Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math. 77 (1955), 778–782. MR 72877, DOI 10.2307/2372597
- Andrew S. Dancer and Róbert Szöke, Symmetric spaces, adapted complex structures and hyper-Kähler structures, Quart. J. Math. Oxford Ser. (2) 48 (1997), no. 189, 27–38. MR 1439696, DOI 10.1093/qmath/48.1.27
- Jiri Dadok, On the $C^{\infty }$ Chevalley’s theorem, Adv. in Math. 44 (1982), no. 2, 121–131. MR 658537, DOI 10.1016/0001-8708(82)90002-0
- Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Graduate Studies in Mathematics, vol. 34, American Mathematical Society, Providence, RI, 2001. Corrected reprint of the 1978 original. MR 1834454, DOI 10.1090/gsm/034
- Sigurdur Helgason, Groups and geometric analysis, Mathematical Surveys and Monographs, vol. 83, American Mathematical Society, Providence, RI, 2000. Integral geometry, invariant differential operators, and spherical functions; Corrected reprint of the 1984 original. MR 1790156, DOI 10.1090/surv/083
- Harish-Chandra, Spherical functions on a semisimple Lie group. I, Amer. J. Math. 80 (1958), 241–310. MR 94407, DOI 10.2307/2372786
- Domingo Luna, Fonctions différentiables invariantes sous l’opération d’un groupe réductif, Ann. Inst. Fourier (Grenoble) 26 (1976), no. 1, ix, 33–49 (French, with English summary). MR 423398
- Peter W. Michor, Basic differential forms for actions of Lie groups, Proc. Amer. Math. Soc. 124 (1996), no. 5, 1633–1642. MR 1307550, DOI 10.1090/S0002-9939-96-03195-4
- Peter W. Michor, Basic differential forms for actions of Lie groups. II, Proc. Amer. Math. Soc. 125 (1997), no. 7, 2175–2177. MR 1401750, DOI 10.1090/S0002-9939-97-03929-4
- Gerald W. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975), 63–68. MR 370643, DOI 10.1016/0040-9383(75)90036-1
- Louis Solomon, Invariants of finite reflection groups, Nagoya Math. J. 22 (1963), 57–64. MR 154929, DOI 10.1017/S0027763000011028
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 Szőke
- Affiliation: Department of Analysis, Eötvös University, Pázmány Péter sétány 1/c, Budapest, 1117 Hungary
- Email: rszoke@cs.elte.hu
- Received by editor(s): July 24, 2004
- Received by editor(s) in revised form: July 4, 2005
- Published electronically: 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 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 3449-3456
- MSC (2000): Primary 20F55, 22E46, 53C35
- DOI: https://doi.org/10.1090/S0002-9939-06-08589-3
- MathSciNet review: 2240655