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Weight representations of affine Kac-Moody algebras and small quantum groups
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abstract
We study the weight modules over affine Kac-Moody algebras from the view point of vertex algebras, and determine the abelian category of weight modules for the simple affine vertex algebra $L_k(\mathfrak{sl}_2)$ at any non-integral admissible level $k$. In particular, we show that the principal block of the category of weight modules over admissible $L_k(\mathfrak{sl}_2)$ is equivalent to that of the corresponding (unrolled) small quantum group.
Forward citations
Cited by 3 Pith papers
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Ribbon categories of weight modules for affine $\mathfrak{sl}_2$ at admissible levels
Rigidity is proven for the braided tensor category of finitely-generated weight modules of affine sl2 at all admissible levels, upgrading it to a ribbon category.
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Fusion rules and rigidity for weight modules over the simple admissible affine $\mathfrak{sl}(2)$ and $\mathcal{N}=2$ superconformal vertex operator superalgebras
Rigidity of weight module categories for admissible affine sl(2) and N=2 superconformal minimal models is proved, together with the conjectured fusion product decompositions, including non-semisimple summands.
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On Virasoro-type reductions and inverse Hamiltonian reductions for $W$-algebras and $W_\infty$-algebras
Virasoro-type reduction and inverse Hamiltonian reduction are established for height-two W-algebras in classical Lie types and for the universal W∞-algebra W^{sp}_∞.
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