Cartan Determinants and Shapovalov forms

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dc.creatorBrundan, Jonathan
dc.creatorKleshchev, Alexander
dc.date2001-11-29
dc.date.accessioned2026-07-07T04:44:51Z
dc.date.available2026-07-07T04:44:51Z
dc.descriptionWe compute the determinant of the Gram matrix of the Shapovalov form on weight spaces of the basic representation of an affine Kac-Moody algebra of ADE type (possibly twisted). As a consequence, we obtain explicit formulae for the determinants of the Cartan matrices of $p$-blocks of the symmetric group and its double cover, and of the associated Hecke algebras at roots of unity.
dc.identifierhttps://arxiv.org/abs/math/0111306
dc.identifierhttp://arxiv.org/abs/math/0111306
dc.identifierMath. Ann. 324 (2002), 431-449.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62761
dc.subjectRepresentation Theory
dc.subject17B67; 20G05
dc.titleCartan Determinants and Shapovalov forms
dc.typetext

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