On a property of branching coefficients for affine Lie algebras

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dc.creatorIlyin, Mikhail
dc.creatorKulish, Petr
dc.creatorLyakhovsky, Vladimir
dc.date2008-12-11
dc.date.accessioned2026-07-07T12:11:59Z
dc.date.available2026-07-07T12:11:59Z
dc.descriptionIt is demonstrated that decompositions of integrable highest weight modules of a simple Lie algebra with respect to its reductive subalgebra obey the set of algebraic relations leading to the recursive properties for the corresponding branching coefficients. These properties are encoded in the special element (of the formal algebra E(g)) Gamma_(a ->g) that describes the injection and is called the fan. In the simplest case, when "a" is a Cartan subalgebra of g, the recursion procedure generates the weight diagram of the module L(g). When applied to a reduction of highest weight modules the recursion described by the fan provides a highly effective tool to obtain the explicit values of branching coefficients.
dc.description17 pages, 3 figures, to be published in Algebra i Analiz
dc.identifierhttps://arxiv.org/abs/0812.2124
dc.identifierhttp://arxiv.org/abs/0812.2124
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210400
dc.subjectRepresentation Theory
dc.subjectMathematical Physics
dc.subject17B67 (Primary), 17B10 (Secondary)
dc.titleOn a property of branching coefficients for affine Lie algebras
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