A new modular plethystic $\mathrm{SL}_2(\mathbb{F})$-isomorphism $\mathrm{Sym}^{N-1}E \otimes \bigwedge^{N+1} \mathrm{Sym}^{d+1}E \cong Δ^{(2,1^{N-1})} \mathrm{Sym}^d E$

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