Frobenius-Schur indicators for semisimple Lie algebras

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dc.creatorAbu-Hamed, Mohammad
dc.creatorGelaki, Shlomo
dc.date2007-04-02
dc.date.accessioned2026-07-07T07:54:22Z
dc.date.available2026-07-07T07:54:22Z
dc.descriptionLet g be a finite dimensional complex semisimple Lie algebra, and let V be a finite dimensional represenation of g. We give a closed formula for the mth Frobenius-Schur indicator, m>1, of V in representation-theoretic terms. We deduce that the indicators take integer values, and that for a large enough m, the mth indicator of V equals the dimension of the zero weight space of V. For the classical Lie algebras sl(n), so(2n), so(2n+1) and sp(2n), this is the case for m greater or equal to 2n-1, 4n-5, 4n-3 and 2n+1, respectively.
dc.description12 pages, to appear in Journal of Algebra
dc.identifierhttps://arxiv.org/abs/0704.0165
dc.identifierhttp://arxiv.org/abs/0704.0165
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126582
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.titleFrobenius-Schur indicators for semisimple Lie algebras
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