Type A fusion rules from elementary group theory

Details Type A fusion rules from elementary group theory Type A fusion rules from elementary group theory

2000-12-20

arxiv.org/abs/math/0012194v1

Mathematics

Quantum Algebra

19 pages, AMS-TeX, includes and uses the 'cellular' TeX macro package for tables. Available from ftp://ftp.math.binghamton.e

Scientific paper

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)\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].

Affiliated with

Also associated with

No associations

Rating

Type A fusion rules from elementary group theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Type A fusion rules from elementary group theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Type A fusion rules from elementary group theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-374903