Rationality of admissible affine vertex algebras in the category \(\mathcal O\)

DOI10.1215/00127094-3165113zbMath1395.17057arXiv1207.4857OpenAlexW1619517239MaRDI QIDQ5963489

Tomoyuki Arakawa

Publication date: 22 February 2016

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4857

zbMATH Keywords

vertex operator algebrasaffine Kac-Moody algebrasJoseph's characteristic varietyKac-Wakimoto admissible representations

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Vertex operators; vertex operator algebras and related structures (17B69) Cohomology of Lie (super)algebras (17B56)

Related Items (45)

Weight representations of admissible affine vertex algebras ⋮ An admissible level \(\widehat{\mathfrak{osp}}(1| 2)\)-model: modular transformations and the Verlinde formula ⋮ 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 \(a_{2}^{(1)}\) ⋮ Direct limit completions of vertex tensor categories ⋮ On the semisimplicity of the category \(KL_k\) for affine Lie superalgebras ⋮ Two-sided BGG resolutions of admissible representations ⋮ \(A_{2l}^{(2)}\) at level \(-l-\frac{1}{2}\) ⋮ Snowflake modules and Enright functor for Kac-Moody superalgebras ⋮ Positive energy representations of affine vertex algebras ⋮ Braided tensor categories of admissible modules for affine Lie algebras ⋮ Conformal embeddings of affine vertex algebras in minimal \(W\)-algebras. II: Decompositions ⋮ Sheets and associated varieties of affine vertex algebras ⋮ Admissible representations of simple affine vertex algebras ⋮ A Kazhdan-Lusztig correspondence for \(L_{-\frac{3}{2}}(\mathfrak{sl}_3)\) ⋮ On the nilpotent orbits arising from admissible affine vertex algebras ⋮ Full Logarithmic Conformal Field theory — an Attempt at a Status Report ⋮ Higgs and Coulomb branches from vertex operator algebras ⋮ Rigid tensor structure on big module categories for some \(W\)-(super)algebras in type \(A\) ⋮ Subregular W-algebras of type A ⋮ Rationality of affine vertex operator superalgebras with rational conformal weights ⋮ Tensor category \(\mathrm{KL}_k (\mathfrak{sl}_{2n})\) via minimal affine \(W\)-algebras at the non-admissible level \(k = - \frac{2n + 1}{2}\) ⋮ Rationality and fusion rules of exceptional \(\mathcal{W}\)-algebras ⋮ Bershadsky-Polyakov vertex algebras at positive integer levels and duality ⋮ Mini-workshop: Recent developments in representation theory and mathematical physics. Abstracts from the mini-workshop held March 20--26, 2022 ⋮ JOSEPH IDEALS AND LISSE MINIMAL -ALGEBRAS ⋮ Rectangular W-algebras, extended higher spin gravity and dual coset CFTs ⋮ Realizations of simple affine vertex algebras and their modules: the cases \({\widehat{sl(2)}}\) and \({\widehat{osp(1,2)}}\) ⋮ Fusion categories for affine vertex algebras at admissible levels ⋮ Generators, spanning sets and existence of twisted modules for a grading-restricted vertex (super)algebra ⋮ Associated varieties and Higgs branches (a survey) ⋮ Classifying relaxed highest-weight modules for admissible-level Bershadsky-Polyakov algebras ⋮ Tensor categories of affine Lie algebras beyond admissible levels ⋮ Relaxed highest-weight modules. III: Character formulae ⋮ Generalized parafermions of orthogonal type ⋮ Schur-Weyl duality for Heisenberg cosets ⋮ Modularity of relatively rational vertex algebras and fusion rules of principal affine \(W\)-algebras ⋮ Module category and \(C_2\)-cofiniteness of affine vertex operator superalgebras ⋮ Gluing vertex algebras ⋮ \(W\)-algebras as coset vertex algebras ⋮ Trialities of orthosymplectic \(\mathcal{W} \)-algebras ⋮ Admissible-level \(\mathfrak{sl}_3\) minimal models ⋮ Relaxed highest-weight modules II: Classifications for affine vertex algebras ⋮ Urod algebras and Translation of W-algebras ⋮ On the representation theory of the vertex algebra L−5/2(sl(4))

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