The paper develops a formalism for reduction and inverse-reduction functors and computes the action of reduction on standard modules of V^k(sl_2), noting unbounded spectral sequences.
Quantum Langlands duality of representations ofW-algebras.Contemporary Mathematics, 155:2235–2262, 2019.arXiv:1807.01536 [math.QA]
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Reduction and inverse-reduction functors I: standard $\mathsf{V^k}(\mathfrak{sl}_2)$-modules
The paper develops a formalism for reduction and inverse-reduction functors and computes the action of reduction on standard modules of V^k(sl_2), noting unbounded spectral sequences.