2021
DOI: 10.1007/s00220-021-04008-y
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Classifying Relaxed Highest-Weight Modules for Admissible-Level Bershadsky–Polyakov Algebras

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Cited by 12 publications
(11 citation statements)
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“…The remainder of Section 4.2 then addresses how the highest-weight modules are related by the conjugation and spectral flow functors. This will be important for the standard module analysis in [34]. Section 4.3 then lifts this classification to simple relaxed highest-weight BP k -modules, establishing Main Theorem 3.…”
mentioning
confidence: 82%
See 1 more Smart Citation
“…The remainder of Section 4.2 then addresses how the highest-weight modules are related by the conjugation and spectral flow functors. This will be important for the standard module analysis in [34]. Section 4.3 then lifts this classification to simple relaxed highest-weight BP k -modules, establishing Main Theorem 3.…”
mentioning
confidence: 82%
“…They, along with their spectral flows, are also the building blocks (the "atypical standards") for the resolutions that underpin the so-called standard module formalism [32,33] for modular transformations and Verlinde formulae for nonrational vertex operator algebras. We intend to return to this in a forthcoming paper [34]. 1.3.…”
mentioning
confidence: 99%
“…Let W k be the simple quotient of W k and let k / ∈ Z ≥0 . It has been studied at admissible level [3,11,41]. We can use the free field realization to prove the following results:…”
Section: Introductionmentioning
confidence: 99%
“…Here we briefly recall the relation between paths in the fine moduli space of complex structures and families of complex curves with base given by an interval. We then consider families of C-extended surfaces with complex structure to formulate the compatibility of the isomorphism (42) with transport along paths.…”
Section: Compatibility With Transportmentioning
confidence: 99%
“…Write Σ c := γ(0) and Σ c := γ(1), so that when forgetting the complex structure on the fibres, E γ defines a bordism Σ −→ Σ. The isomorphism (42) is compatible with transport along E γ in the following sense: parallel transport via the projectively flat connection on the bundle of conformal blocks gives a linear isomorphism where the two sides may differ by a multiplicative constant. Finally, we need to say how both sides of (42) behave under changing the order of the n marked points on Σ c by some permutation π ∈ S n .…”
Section: Compatibility With Transportmentioning
confidence: 99%