Reflection groups acting on their hyperplanes

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dc.creatorMarin, Ivan
dc.date2008-09-02
dc.date.accessioned2026-07-07T09:59:57Z
dc.date.available2026-07-07T09:59:57Z
dc.descriptionAfter having established elementary results on the relationship between a finite complex (pseudo-)reflection group W < GL(V) and its reflection arrangement A, we prove that the action of W on A is canonically related with other natural representations of W, through a `periodic' family of representations of its braid group. We also prove that, when W is irreducible, then the squares of defining linear forms for A span the quadratic forms on V, which imply |A| >= n(n+1)/2 for n = dim V, and relate the W-equivariance of the corresponding map with the period of our family.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/0809.0384
dc.identifierhttp://arxiv.org/abs/0809.0384
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168208
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.subject20F55, 20C15,52C35, 15A63
dc.titleReflection groups acting on their hyperplanes
dc.typetext

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