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Jacobians of reflection groups
Author(s):
Julia
Hartmann;
Anne
V.
Shepler
Journal:
Trans. Amer. Math. Soc.
360
(2008),
123-133.
MSC (2000):
Primary 13A50, 20F55;
Secondary 52C35
Posted:
August 6, 2007
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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
DOI:
10.1090/S0002-9947-07-04379-6
PII:
S 0002-9947(07)04379-6
Keywords:
Invariant theory,
Jacobian determinant,
modular,
Coxeter group,
reflection group,
hyperplane arrangement,
pointwise stabilizer
Received by editor(s):
April 14, 2005
Received by editor(s) in revised form:
August 18, 2005
Posted:
August 6, 2007
Additional Notes:
The work of the second author was partially supported by National Security Agency grant MDA904-03-1-0005
Copyright of article:
Copyright
2007,
American Mathematical Society
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