su(N) tensor product multiplicities and virtual Berenstein-Zelevinsky triangles

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dc.creatorRasmussen, Jorgen
dc.creatorWalton, Mark A.
dc.date2000-10-31
dc.date2001-12-12
dc.date.accessioned2026-07-07T10:54:11Z
dc.date.available2026-07-07T10:54:11Z
dc.descriptionInformation on su(N) tensor product multiplicities is neatly encoded in Berenstein-Zelevinsky triangles. Here we study a generalisation of these triangles by allowing negative as well as non-negative integer entries. For a fixed triple product of weights, these generalised Berenstein-Zelevinsky triangles span a lattice in which one may move by adding integer linear combinations of so-called virtual triangles. Inequalities satisfied by the coefficients of the virtual triangles describe a polytope. The tensor product multiplicities may be computed as the number of integer points in this convex polytope. As our main result, we present an explicit formula for this discretised volume as a multiple sum. As an application, we also address the problem of determining when a tensor product multiplicity is non-vanishing. The solution is represented by a set of inequalities in the Dynkin labels. We also allude to the question of when a tensor product multiplicity is greater than a given non-negative integer.
dc.description12 pages, LaTeX, version to be published
dc.identifierhttps://arxiv.org/abs/math-ph/0010051
dc.identifierhttp://arxiv.org/abs/math-ph/0010051
dc.identifierJ.Phys.A34:11095-11105,2001
dc.identifierdoi:10.1088/0305-4470/34/49/324
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185727
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectRepresentation Theory
dc.titlesu(N) tensor product multiplicities and virtual Berenstein-Zelevinsky triangles
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