Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Bases of the contact-order filtration of derivations of Coxeter arrangements

Author: Hiroaki Terao
Journal: Proc. Amer. Math. Soc. 133 (2005), 2029-2034
MSC (2000): Primary 32S22
Published electronically: January 21, 2005
Erratum: Proc. Amer. Math. Soc. 136 (2008), 2639
MathSciNet review: 2099414
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. Bourbaki, N.: Groupes et Algèbres de Lie. Chapitres 4,5 et 6, Hermann, Paris, 1968 MR 0240238 (39:1590)
  • 2. Dubrovin, B.: Geometry of 2D topological field theories. In: ``Integrable systems and quantum groups'' (ed. Francaviglia, M., Greco, S.), Lectures at C.I.M.E., 1993, LNM 1620, Springer, Berlin-Heidelberg-New York, 1996, pp. 120-348 MR 1397274 (97d:58038)
  • 3. Orlik, P., Terao, H.: Arrangements of Hyperplanes. Grundlehren der Math. Wiss. 300, Springer Verlag, 1992 MR 1217488 (94e:52014)
  • 4. Saito, K.: On a linear structure of the quotient variety by a finite reflexion group. RIMS Kyoto preprint 288, 1979 = Publ. Res. Inst. Math. Sci. 29 (1993) 535-579 MR 1245441 (94k:32059)
  • 5. Saito, K.: Finite reflection groups and related geometry (A motivation to the period mapping for primitive forms). preprint, 2000
  • 6. Terao, H.: Multiderivations of Coxeter arrangements. Inventiones Math., 148 (2002) 659-674 MR 1908063 (2003h:20074)
  • 7. Terao, H.: The Hodge filtration and the contact-order filtration of derivations of Coxeter arrangements. preprint 2002 (math.CO/0205058)
  • 8. Yoshinaga, M.: The primitive derivation and freeness of multi-Coxeter arrangements. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 7, 116-119 MR 1930214 (2003k:32039)
  • 9. Yoshinaga, M.: Characterization of a free arrangement and conjecture of Edelman and Reiner. Inventiones Math., 157 (2004), 449-454. MR 2077250
  • 10. Ziegler, G. M.: Multiarrangements of hyperplanes and their freeness. In: Singularities. Contemporary Math. 90, Amer. Math. Soc., 1989, pp. 345-359 MR 1000610 (90e:32015)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32S22

Retrieve articles in all journals with MSC (2000): 32S22

Additional Information

Hiroaki Terao
Affiliation: Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan

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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society