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On the structure of W-algebras in type A
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We formulate and prove examples of a conjecture which describes the W-algebras in type A as successive quantum Hamiltonian reductions of affine vertex algebras associated with several hook-type nilpotent orbits. This implies that the affine coset subalgebras of hook-type W-algebras are building blocks of the W-algebras in type A. In the rational case, it turns out that the building blocks for the simple quotients are provided by the minimal series of the regular W-algebras. In contrast, they are provided by singlet-type extensions of W-algebras at collapsing levels which are irrational. In the latter case, several new sporadic isomorphisms between different W-algebras are established.
Forward citations
Cited by 3 Pith papers
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Reduction by stages for affine W-algebras
Reduction by stages holds for affine W-algebras: under conditions (⋆), W_k(g,f2) is the BRST cohomology of W_k(g,f1) with respect to f0 = f2 - f1.
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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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On Kazama-Suzuki Duality between $\mathcal{W}_k(\mathfrak{sl}_4, f_{\rm sub})$ and $N=2$ Superconformal Vertex Algebra
The subregular W-algebra W_{-1}(sl4,f_sub) and the N=2 superconformal algebra at c=-15 are shown to be Kazama-Suzuki dual, giving a complete classification of irreducible highest-weight W_{-1}(sl4,f_sub)-modules.
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