Type A fusion rules from elementary group theory

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dc.creatorFeingold, Alex J.
dc.creatorWeiner, Michael D.
dc.date2000-12-20
dc.date.accessioned2026-07-07T04:39:19Z
dc.date.available2026-07-07T04:39:19Z
dc.descriptionWe show how the fusion rules for an affine Kac-Moody Lie algebra g of type A_{n-1}, n = 2 or 3, for all positive integral level k, can be obtained from elementary group theory. The orbits of the kth symmetric group, S_k, acting on k-tuples of integers modulo n, Z_n^k, are in one-to-one correspondence with a basis of the level k fusion algebra for g. If [a],[b],[c] are any three orbits, then S_k acts on T([a],[b],[c]) = {(x,y,z)\in [a]x[b]x[c] such that x+y+z=0}, which decomposes into a finite number, M([a],[b],[c]), of orbits under that action. Let N = N([a],[b],[c]) denote the fusion coefficient associated with that triple of elements of the fusion algebra. For n = 2 we prove that M([a],[b],[c]) = N, and for n = 3 we prove that M([a],[b],[c]) = N(N+1)/2. This extends previous work on the fusion rules of the Virasoro minimal models [Akman, Feingold, Weiner, Minimal model fusion rules from 2-groups, Letters in Math. Phys. 40 (1997), 159-169].
dc.description19 pages, AMS-TeX, includes and uses the 'cellular' TeX macro package for tables. Available from ftp://ftp.math.binghamton.edu/pub/alex/typeAFusion.dvi.Z or from http://www.math.binghamton.edu/alex/ . Submitted to Proceedings of a Conference on Infinite-Dimensional Lie Theory and Field Theory, Charlottesville, VA, May 23-27, 2000, Contemporary Mathematics
dc.identifierhttps://arxiv.org/abs/math/0012194
dc.identifierhttp://arxiv.org/abs/math/0012194
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60617
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subject17B67, 17B65, 81T40 (Primary) 81R10, 05E10 (Secondary)
dc.titleType A fusion rules from elementary group theory
dc.typetext

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