Explicit generators in rectangular affine \(\mathcal {W}\)-algebras of type \(A\)

DOI10.1007/s11005-016-0890-2zbMath1415.17027arXiv1403.1017OpenAlexW3125776676MaRDI QIDQ2361094

Tomoyuki Arakawa, Alexander I. Molev

Publication date: 29 June 2017

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.1017

zbMATH Keywords

Miura transformationvertex algebraaffine \(W\)-algebra

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Vertex operators; vertex operator algebras and related structures (17B69)

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Affine super Yangians and rectangular W-superalgebras ⋮ On certain 𝑊-algebras of type 𝒲_{𝓀}(𝔰𝔩₄,𝔣) ⋮ Screening operators and parabolic inductions for affine \(\mathcal{W}\)-algebras ⋮ W-algebras for Argyres-Douglas theories ⋮ Quiver Yangians and -algebras for generalized conifolds ⋮ More on affine Dynkin quiver Yangians ⋮ Rationality and fusion rules of exceptional \(\mathcal{W}\)-algebras ⋮ Higher Airy structures and topological recursion for singular spectral curves ⋮ Coset vertex operator algebras and \(\mathcal W\)-algebras of \(A\)-type ⋮ Generators of supersymmetric classical \(W\)-algebras ⋮ Supersymmetric \(W\)-algebras ⋮ Rectangular W-algebras, extended higher spin gravity and dual coset CFTs ⋮ The Grassmannian VOA ⋮ Classical \(\mathcal W\)-algebras in types \(A\), \(B\), \(C\), \(D\) and \(G\) ⋮ Strong generators of the subregular \(\mathcal{W}\)-algebra \(\mathcal{W}^{K-N}(\mathfrak{sl}_N, f_{\text{sub}})\) and combinatorial description at critical level ⋮ Higher-rank isomonodromic deformations and \(W\)-algebras ⋮ The matrix-extended \({\mathcal{W}}_{1+\infty}\) algebra ⋮ Schur-Weyl duality for Heisenberg cosets ⋮ Deformed \(W\)-algebras in type \(A\) for rectangular nilpotent ⋮ Coproduct for affine Yangians and parabolic induction for rectangular \(W\)-algebras ⋮ On even spin \({\mathcal{W}}_{\infty }\) ⋮ Parafermion vertex operator algebras and $W$-algebras

Cites Work

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• Quantization of the Drinfel'd-Sokolov reduction.
• Rationality of \(W\)-algebras: principal nilpotent cases
• Quantum reduction and representation theory of superconformal algebras
• Representation theory of superconformal algebras and the Kac-Roan-Wakimoto conjecture
• Shifted Yangians and finite \(W\)-algebras
• Quantum reduction for affine superalgebras
• Yangian realisations from finite \({\mathcal W}\)-algebras
• Classical \(\mathcal W\)-algebras in types \(A\), \(B\), \(C\), \(D\) and \(G\)
• Representation theory of \(\mathcal{W}\)-algebras
• RTT presentation of finite 𝒲-algebras

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