The Sign Representation for Shephard Groups

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dc.creatorOrlik, Peter
dc.creatorReiner, Victor
dc.creatorShepler, Anne V.
dc.date2000-11-15
dc.date.accessioned2026-07-07T04:38:36Z
dc.date.available2026-07-07T04:38:36Z
dc.descriptionShephard groups are unitary reflection groups arising as the symmetries of regular complex polytopes. For a Shephard group, we identify the representation carried by the principal ideal in the coinvariant algebra generated by the image of the product of all linear forms defining reflecting hyperplanes. This representation turns out to have many equivalent guises making it analogous to the sign representation of a finite Coxeter group. One of these guises is (up to a twist) the cohomology of the Milnor fiber for the isolated singularity at 0 in the hypersurface defined by any homogeneous invariant of minimal degree.
dc.descriptionSubmitted. 13 pages
dc.identifierhttps://arxiv.org/abs/math/0011105
dc.identifierhttp://arxiv.org/abs/math/0011105
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60346
dc.subjectGroup Theory
dc.subjectCombinatorics
dc.subjectGeometric Topology
dc.subjectRepresentation Theory
dc.subject20F55, 52B30, 32S55
dc.titleThe Sign Representation for Shephard Groups
dc.typetext

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