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Confusion about Wakimoto's chiral differential operators on $\mathbf{P}^1$
It is a classical result of Wakimoto that the sheaf of chiral differential operators $D_{ch}$ on $\mathbf{P}^1$ has global sections
$$D_{ch}(\mathbf{P}^1)\ \simeq\ L_{-2}(\mathfrak{sl}_2)$$
the simple ...
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