The Polynomial Behavior of Weight Multiplicities for the Affine Kac-Moody Algebras $A^{(1)}_r$

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dc.creatorBenkart, Georgia
dc.creatorKang, Seok-Jin
dc.creatorLee, Hyeonmi
dc.creatorMisra, Kailash C.
dc.creatorShin, Dong-Uy
dc.date1998-09-06
dc.date.accessioned2026-07-07T05:25:54Z
dc.date.available2026-07-07T05:25:54Z
dc.descriptionWe prove that the multiplicity of an arbitrary dominant weight for an integrable highest weight representation of the affine Kac-Moody algebra $A_{r}^{(1)}$ is a polynomial in the rank $r$. In the process we show that the degree of this polynomial is less than or equal to the depth of the weight with respect to the highest weight. These results allow weight multiplicity information for small ranks to be transferred to arbitrary ranks.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/math/9809026
dc.identifierhttp://arxiv.org/abs/math/9809026
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77357
dc.subjectRepresentation Theory
dc.subject17B67, 17B65
dc.titleThe Polynomial Behavior of Weight Multiplicities for the Affine Kac-Moody Algebras $A^{(1)}_r$
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