Frobenius-Schur Indicators for Subgroups and the Drinfel'd Double of Weyl Groups

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dc.creatorGuralnick, Robert
dc.creatorMontgomery, Susan
dc.date2007-03-22
dc.date.accessioned2026-07-07T07:53:24Z
dc.date.available2026-07-07T07:53:24Z
dc.descriptionIf G is a finite group and k is a field, there is a natural construction of a Hopf algebra over k associated to G, the Drinfel'd double D(G). We prove that if G is any finite real reflection group with Drinfel'd double D(G) over an algebraically closed field k of characteristic not 2, then every simple D(G)-module has Frobenius-Schur indicator +1. This generalizes the classical results for modules over the group itself. We also prove some new results about Weyl groups. In particular, we prove that any abelian subgroup is inverted by some involution. Also, if E is any elementary abelian 2-subgroup of the Weyl group W, then all representations of the centralizer of E in W are defined over the rational field.
dc.identifierhttps://arxiv.org/abs/math/0703681
dc.identifierhttp://arxiv.org/abs/math/0703681
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126239
dc.subjectQuantum Algebra
dc.subjectGroup Theory
dc.subjectRepresentation Theory
dc.subject16W30; 20C15, 20G42
dc.titleFrobenius-Schur Indicators for Subgroups and the Drinfel'd Double of Weyl Groups
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