Representation theory of superconformal algebras and the Kac-Roan-Wakimoto conjecture
From MaRDI portal
Publication:812552
DOI10.1215/S0012-7094-05-13032-0zbMath1112.17026arXivmath-ph/0405015OpenAlexW3006404479WikidataQ122873368 ScholiaQ122873368MaRDI QIDQ812552
Publication date: 24 January 2006
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math-ph/0405015
Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Virasoro and related algebras (17B68) Vertex operators; vertex operator algebras and related structures (17B69) Homological methods in Lie (super)algebras (17B55)
Related Items
Affine super Yangians and rectangular W-superalgebras, Explicit generators in rectangular affine \(\mathcal {W}\)-algebras of type \(A\), Screening operators for \(\mathcal {W}\)-algebras, A realisation of the Bershadsky-Polyakov algebras and their relaxed modules, A realization of certain modules for the \(N = 4\) superconformal algebra and the affine Lie algebra \(a_{2}^{(1)}\), Representations of affine superalgebras and mock theta functions. II, Modular linear differential equations of fourth order and minimal \(\mathcal{W}\)-algebras, On the semisimplicity of the category \(KL_k\) for affine Lie superalgebras, Simplicity of vacuum modules over affine Lie superalgebras, Two-sided BGG resolutions of admissible representations, The vertex algebras \(\mathcal{R}^{(p)}\) and \(\mathcal{V}^{(p)}\), On simplicity of vacuum modules, Conformal embeddings of affine vertex algebras in minimal \(W\)-algebras. II: Decompositions, Rationality of Bershadsky-Polyakov vertex algebras, Sheets and associated varieties of affine vertex algebras, Cosets of Bershadsky-Polyakov algebras and rational \({\mathcal W}\)-algebras of type \(A\), Modularity of Bershadsky-Polyakov minimal models, Representations of superconformal algebras and mock theta functions, Quantizing Mishchenko–Fomenko subalgebras for centralizers via affine $W$-algebras, On complete reducibility for infinite-dimensional Lie algebras, A note on quiver Yangians and \(\mathcal{R}\)-matrices, A chiral Borel-Weil-Bott theorem, Subregular W-algebras of type A, Tensor category \(\mathrm{KL}_k (\mathfrak{sl}_{2n})\) via minimal affine \(W\)-algebras at the non-admissible level \(k = - \frac{2n + 1}{2}\), Unitarity of minimal \(W\)-algebras and their representations. I, Defining relations for minimal unitary quantum affine W-algebras, Conformal embeddings of affine vertex algebras in minimal \(W\)-algebras. I: Structural results, On the irreducibility of associated varieties of \(W\)-algebras, JOSEPH IDEALS AND LISSE MINIMAL -ALGEBRAS, Coset vertex operator algebras and \(\mathcal W\)-algebras of \(A\)-type, Relaxed category and vanishing of cohomology associated with quantum reduction, Quantum $q$-Langlands Correspondence, Rationality of \(W\)-algebras: principal nilpotent cases, Representations of affine superalgebras and mock theta functions, Simplicity of vacuum modules and associated varieties, Classifying relaxed highest-weight modules for admissible-level Bershadsky-Polyakov algebras, Finite vs affine \(W\)-algebras, Tensor categories of affine Lie algebras beyond admissible levels, Quantum Langlands duality of representations of -algebras, Trialities of orthosymplectic \(\mathcal{W} \)-algebras, Admissible-level \(\mathfrak{sl}_3\) minimal models, Urod algebras and Translation of W-algebras, Characters and quantum reduction for orthosymplectic Lie superalgebras, Rationality of the exceptional \(\mathcal{W}\)-algebras \(\mathcal{W}_k(\mathfrak{sp}_4,f_{subreg})\) associated with subregular nilpotent elements of \(\mathfrak{sp}_4\)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Quantization of the Drinfel'd-Sokolov reduction.
- Quantum reduction and representation theory of superconformal algebras
- Korteweg-de Vries superequation related to the Lie superalgebra of Neveu-Schwarz-2 string theory
- Vertex operator algebras associated to representations of affine and Virasoro algebras
- Characters and fusion rules for \(W\)-algebras via quantized Drinfeld- Sokolov reduction
- Quantum reduction for affine superalgebras
- Conformal field theories via Hamiltonian reduction
- Modular invariant representations of infinite-dimensional Lie algebras and superalgebras
- AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS
- Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction
