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A new $SL_2$-action on the rank-two $βγ$-system
We construct an explicit rational \(\mathrm{SL}_2(\mathbb C)\)-action on the underlying vector space of the rank-two \(βγ\)-system. The construction is motivated by Creutzig's branching decomposition with respect to \(L_{-1}(\mathfrak{sl}_2)\) and a rank-one Heisenberg vertex algebra. We realize the
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