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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Jacobians of reflection groups
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by Julia Hartmann and Anne V. Shepler PDF
Trans. Amer. Math. Soc. 360 (2008), 123-133 Request permission

Abstract:

Steinberg showed that when a finite reflection group acts on a real or complex vector space of finite dimension, the Jacobian determinant of a set of basic invariants factors into linear forms which define the reflecting hyperplanes. This result generalizes verbatim to fields whose characteristic is prime to the order of the group. Our main theorem gives a generalization of Steinberg’s result for groups with a polynomial ring of invariants over arbitrary fields using a ramification formula of Benson and Crawley-Boevey.
References
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Additional Information
  • Julia Hartmann
  • Affiliation: IWR, Universität Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany
  • Email: Julia.Hartmann@iwr.uni-heidelberg.de
  • Anne V. Shepler
  • Affiliation: Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, Texas 76203
  • Email: ashepler@unt.edu
  • Received by editor(s): April 14, 2005
  • Received by editor(s) in revised form: August 18, 2005
  • Published electronically: August 6, 2007
  • Additional Notes: The work of the second author was partially supported by National Security Agency grant MDA904-03-1-0005
  • © Copyright 2007 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 123-133
  • MSC (2000): Primary 13A50, 20F55; Secondary 52C35
  • DOI: https://doi.org/10.1090/S0002-9947-07-04379-6
  • MathSciNet review: 2341996