Jacobians of Reflection Groups

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dc.creatorHartmann, Julia
dc.creatorShepler, Anne V.
dc.date2004-05-07
dc.date.accessioned2026-07-07T05:08:01Z
dc.date.available2026-07-07T05:08:01Z
dc.descriptionSteinberg 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 arbitrary fields using a ramification formula of Benson and Crawley-Boevey. As an intermediate result, we show that every finite group which fixes a hyperplane pointwise has a polynomial ring of invariants.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0405135
dc.identifierhttp://arxiv.org/abs/math/0405135
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71096
dc.subjectRepresentation Theory
dc.subjectCommutative Algebra
dc.subject13A50, 20C, 52C35
dc.titleJacobians of Reflection Groups
dc.typetext

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