Geodesic
Canonical Systems of Basic Invariants for Unitary Reflection Groups
Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 617-623

Voir la notice de l'article provenant de la source Cambridge University Press

It is known that there exists a canonical system for every finite real reflection group. In a previous paper, the first and the third authors obtained an explicit formula for a canonical system. In this article, we first define canonical systems for the finite unitary reflection groups, and then prove their existence. Our proof does not depend on the classification of unitary reflection groups. Furthermore, we give an explicit formula for a canonical system for every unitary reflection group.
DOI : 10.4153/CMB-2016-031-7
Mots-clés : 13A50, 20F55, basic invariant, invariant theory, finite unitary reflection group 
Nakashima, Norihiro; Terao, Hiroaki; Tsujie, Shuhei. Canonical Systems of Basic Invariants for Unitary Reflection Groups. Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 617-623. doi: 10.4153/CMB-2016-031-7
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[1] [1] Bourbaki, N., Groupes et Algèbres de Lie. Chapitres 4, 5, et 6, Hermann, Paris, 1968. Google Scholar

[2] [2] Chevalley, C., Invariants of finite groups generated by reflections. Amer. J. Math, 77(1955), no. 4, 778–782. Google Scholar | DOI

[3] [3] Flatto, L., Basic sets of invariants for finite reflection groups. Bull. Amer. Math. Soc. 74(1968), no. 4, 730–734. Google Scholar | DOI

[4] [4] Flatto, L., Invariants of finite reflection groups and mean value problems. II. Amer. J. Math. 92(1970), 552–561. Google Scholar | DOI

[5] [5] Flatto, L. and Wiener, M. M., Invariants of finite reflection groups and mean value problems. Amer. J. Math. 91(1969), no. 3, 591–598. Google Scholar | DOI

[6] [6] Humphreys, J. E., Reflection groups and Coxeter groups. Cambridge Studies in Mathematics, 29, Cambridge University Press, Cambridge, 1990. Google Scholar

[7] [7] Iwasaki, K., Basic invariants of finite reflection groups. J. Algebra. 195(1997), no. 2, 538–547. Google Scholar | DOI

[8] [8] Kane, R., Reflection groups and invariant theory. CMS Books in Mathematics/Ouvragesde Mathématiques de la SMC, 5, Springer-Verlag, New York, 2001. Google Scholar | DOI

[9] [9] Nakashima, N. and Tsujie, S., A canonical system of basic invariants of a finite reflection group. J. Algebra 406(2014), 143–153. Google Scholar | DOI

[10] [10] Orlik, P. and Solomon, L., Unitary reflection groups and cohomology. Invent. Math. 59(1980), no. 1, 77–94. Google Scholar | DOI

[11] [11] Orlik, P. and Terao, H., Arrangements of hyperplanes. Grundlehrendermatematischen Wissenschaften, 300, Springer-Verlag, Berlin, 1992. Google Scholar

[12] [12] Steinberg, R., Differential equations invariant under finite reflection groups. Trans. Amer. Math. Soc. 112(1964), no. 3, 392–400. Google Scholar | DOI

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