Elementary divisors of the Shapovalov form on the basic representation of Kac-Moody algebras

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dc.creatorHill, David
dc.date2006-10-11
dc.date2006-10-11
dc.date.accessioned2026-07-07T10:03:20Z
dc.date.available2026-07-07T10:03:20Z
dc.descriptionWe provide an algorithm to calculate the invariant factors of the Shapovalov form on the standard $\Z$-lattice inside the basic representation of a Kac-Moody algebra of $ADE$ type, and give explicit formulae in some cases. The techniques developed reduce the problem to finding the invariant factors of a family of bilinear forms on the ring of symmetric functions, having Jack's symmetric functions as an orthonormal basis. These results have applications to the representation theory of Iwahori-Hecke algebras at roots of unity and the modular representation theory of symmetric groups.
dc.identifierhttps://arxiv.org/abs/math/0610376
dc.identifierhttp://arxiv.org/abs/math/0610376
dc.identifierJ. Algebra 319 (2008), 5208-5246
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169253
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.subject17B67; 20G05
dc.titleElementary divisors of the Shapovalov form on the basic representation of Kac-Moody algebras
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