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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Bases of the contact-order filtration of derivations of Coxeter arrangements
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by Hiroaki Terao PDF
Proc. Amer. Math. Soc. 133 (2005), 2029-2034 Request permission

Erratum: Proc. Amer. Math. Soc. 136 (2008), 2639-2639.

Abstract:

In a recent paper, we constructed a basis for the contact-order filtration of the module of derivations on the orbit space of a finite real reflection group acting on an $\ell$-dimensional Euclidean space. Recently M. Yoshinaga constructed another basis for the contact-order filtration. In this note we give an explicit formula relating Yoshinaga’s basis to the basis we constructed earlier. The two bases turn out to be equal (up to a constant matrix).
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
  • Boris Dubrovin, Geometry of $2$D topological field theories, Integrable systems and quantum groups (Montecatini Terme, 1993) Lecture Notes in Math., vol. 1620, Springer, Berlin, 1996, pp. 120–348. MR 1397274, DOI 10.1007/BFb0094793
  • Peter Orlik and Hiroaki Terao, Arrangements of hyperplanes, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 300, Springer-Verlag, Berlin, 1992. MR 1217488, DOI 10.1007/978-3-662-02772-1
  • Kyoji Saito, On a linear structure of the quotient variety by a finite reflexion group, Publ. Res. Inst. Math. Sci. 29 (1993), no. 4, 535–579. MR 1245441, DOI 10.2977/prims/1195166742
  • Saito, K.: Finite reflection groups and related geometry (A motivation to the period mapping for primitive forms). preprint, 2000
  • Hiroaki Terao, Multiderivations of Coxeter arrangements, Invent. Math. 148 (2002), no. 3, 659–674. MR 1908063, DOI 10.1007/s002220100209
  • Terao, H.: The Hodge filtration and the contact-order filtration of derivations of Coxeter arrangements. preprint 2002 (math.CO/0205058)
  • Masahiko Yoshinaga, The primitive derivation and freeness of multi-Coxeter arrangements, Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 7, 116–119. MR 1930214
  • Masahiko Yoshinaga, Characterization of a free arrangement and conjecture of Edelman and Reiner, Invent. Math. 157 (2004), no. 2, 449–454. MR 2077250, DOI 10.1007/s00222-004-0359-2
  • Günter M. Ziegler, Multiarrangements of hyperplanes and their freeness, Singularities (Iowa City, IA, 1986) Contemp. Math., vol. 90, Amer. Math. Soc., Providence, RI, 1989, pp. 345–359. MR 1000610, DOI 10.1090/conm/090/1000610
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Additional Information
  • Hiroaki Terao
  • Affiliation: Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan
  • MR Author ID: 191642
  • Received by editor(s): June 25, 2002
  • Received by editor(s) in revised form: March 1, 2004
  • Published electronically: January 21, 2005
  • Additional Notes: The author was partially supported by the Grant-in-aid for scientific research (Nos. 14340018 and 13874005), the Ministry of Education, Sports, Science and Technology, Japan
  • Communicated by: John R. Stembridge
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 2029-2034
  • MSC (2000): Primary 32S22
  • DOI: https://doi.org/10.1090/S0002-9939-05-07767-1
  • MathSciNet review: 2099414