The moduli space of 𝑆𝑈(3)-flat connections and the fusion rules

Hayashi, Masato

doi:10.1090/S0002-9939-99-04674-2

The moduli space of $SU(3)$-flat connections and the fusion rules
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Proc. Amer. Math. Soc. 127 (1999), 1545-1555 Request permission

Abstract:

The aim of this paper is to determine the existence condition of the moduli space of $SU(3)$-flat connections on $3$-holed $2$-sphere $D$, the so-called pair of pants, and to study its relationship to the $\widehat {\mathfrak {sl}}(3;\mathbb {C})$ fusion rules. The existence condition can be expressed by a system of inequalities with the entries of highest weights with respect to the fundamental weights. This gives a necessary condition for the fusion coefficents to be nontrivial. We also find that the fusion coefficient of a triplet of extremal highest weights equals one. This can be considered a quantum counterpart of the PRV-conjecture.

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