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Type A fusion rules from elementary group theory
[article]
2000
arXiv
pre-print
We 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)∈ [a]x[b]x[c] such that x+y+z=0, which decomposes into a finite number,
arXiv:math/0012194v1
fatcat:5kpr7dnjubhkfi4qqbcsykz4pq