FUSION RULES AND COMPLETE REDUCIBILITY OF CERTAIN MODULES FOR AFFINE LIE ALGEBRAS

DOI10.1142/S021949881350062XzbMath1281.17024arXiv1207.7177WikidataQ115245675 ScholiaQ115245675MaRDI QIDQ5746950

Dražen Adamović, Ozren Perše

Publication date: 11 February 2014

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.7177

zbMATH Keywords

vertex operator algebrabranching rulesfusion rulesaffine Kac-Moody algebrabosonic realization

Mathematics Subject Classification ID

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

Related Items (16)

On the classification of non-equal rank affine conformal embeddings and applications ⋮ Negative index Jacobi forms and quantum modular forms ⋮ Conformal embeddings of affine vertex algebras in minimal \(W\)-algebras. II: Decompositions ⋮ Orbifolds and cosets of minimal \({\mathcal{W}}\)-algebras ⋮ Sheets and associated varieties of affine vertex algebras ⋮ Kostant Pairs of Lie Type and Conformal Embeddings ⋮ Conformal embeddings of affine vertex algebras in minimal \(W\)-algebras. I: Structural results ⋮ On characters of L𝔰𝔩n(−Λ0)-modules ⋮ Conformal embeddings in affine vertex superalgebras ⋮ Finite vs. infinite decompositions in conformal embeddings ⋮ On some vertex algebras related to \(V_{-1}(\mathfrak{sl}(n))\) and their characters ⋮ Universal two-parameter 𝒲_∞-algebra and vertex algebras of type 𝒲(2, 3, …, N) ⋮ Tensor categories of affine Lie algebras beyond admissible levels ⋮ Schur-Weyl duality for Heisenberg cosets ⋮ Corrigendum to: ``Sheets and associated varieties of affine vertex algebras ⋮ On the representation theory of the vertex algebra L−5/2(sl(4))

Cites Work

• Unnamed Item
• Super boson-fermion correspondence
• On quantum Galois theory
• Affine Lie algebras on admissible half-integer levels
• Classical affine algebras
• Vertex operator algebras associated to representations of affine and Virasoro algebras
• Applications of minor summation formulas to rectangular-shaped representations of classical groups
• Classification of irreducible modules for the vertex operator algebra \(M(1)^+\)
• \(\mathcal W_{1+\infty}\) algebra \(\mathcal W_3\) algebra and Friedan-Martinec-Shenker bosonization
• A construction of admissible \(A_1^{(1)}\)-modules of level \(-\frac{4}{3}\)
• A construction of some ideals in affine vertex algebras
• \({\mathcal W}_{1+\infty}\) and \({\mathcal W}(gl_ N)\) with central charge \(N\)
• Vertex operator algebras associated to modular invariant representations for \(A_ 1^{(1)}\)
• Local systems of vertex operators, vertex superalgebras and modules
• Representation theory of the vertex algebra \(W_{1+\infty}\)
• Some general results on conformal embeddings of affine vertex operator algebras
• Representations of certain non-rational vertex operator algebras of affine type
• A note on representations of some affine vertex algebras of type D
• Vertex operator algebras associated to certain admissible modules for affine Lie algebras of type A
• Vertex algebras, Kac-Moody algebras, and the Monster
• Classification of irreducible modules for the vertex operator algebra \(M(1)^+\). II: Higher rank
• Integrable highest weight modules over affine superalgebras and Appell's function

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