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Minimal Model Fusion Rules From 2-Groups

Authors:	Akman Füsun Feingold Alex J Weiner Michael D

Institution:	(1) Department of Mathematics, Utah State University, Logan, UT, 84322, U.S.A;(2) Department of Mathematical Sciences, The State University of New York, Binghamton, NY, 13902-6000, U.S.A;(3) Department of Mathematics, Pennsylvania State University, Altoona, PA, 16601, U.S.A

Abstract:	The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group $G = \mathbb{Z}_2^{p + q - 5}$ in the following manner. There is a partition $G = P_1 \cup \cdot \cdot \cdot \cup P_N$ into disjoint subsets and a bijection between $\{ P_1 ,...,P_N \}$ and the sectors $\{ S_1 ,...,S_N \}$ of the (p,q)-minimal model such that the fusion rules $S_i * S_j = \sum\nolimits_k {D(S_i ,S_j ,S_k )S_k }$ correspond to $P_i * P_j = \sum\nolimits_{k \in T(i,j)} {P_k }$ where $T(i,j) = \{ k\|\exists a \in P_i ,\exists b \in P_j ,a + b \in P_k \}$ .

Keywords:	minimal models fusion rules Virasoro algebra
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