2019
DOI: 10.1007/s00220-019-03328-4
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Realizations of Simple Affine Vertex Algebras and Their Modules: The Cases $${\widehat{sl(2)}}$$ s l ( 2 ) ^ and $${\widehat{osp(1,2)}}$$ o s p ( 1 , 2 ) ^

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Cited by 36 publications
(12 citation statements)
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“…It is widely believed that vertex tensor categories can often also be realized as categories of modules of some (quasi) Hopf algebra. In the case of L ℓ (sl 2 ) -wtmod a close connection to a quantum group of sl 2|1 is expected thanks to the theory of [30] together with the free field realization of [31]. The pioneer of this idea (or better program) is Alyosha Semikhatov [32][33][34].…”
Section: Introductionmentioning
confidence: 99%
“…It is widely believed that vertex tensor categories can often also be realized as categories of modules of some (quasi) Hopf algebra. In the case of L ℓ (sl 2 ) -wtmod a close connection to a quantum group of sl 2|1 is expected thanks to the theory of [30] together with the free field realization of [31]. The pioneer of this idea (or better program) is Alyosha Semikhatov [32][33][34].…”
Section: Introductionmentioning
confidence: 99%
“…This triality are large families of isomorphism of certain coset subVOAs, proven in [CL22a,CL22b]. On the other hand the affine VOA of sl 2 allows for a realization inside the Virasoro algebra times a free field algebra [Ad19].…”
Section: Discussionmentioning
confidence: 98%
“…Sometimes one also has certain chains of conformal embeddings, e.g. the affine VOA of sl 2 at level k embeds into the Virasoro vertex algebra at central charge 13 − 6(k + 2) − 6/(k + 2) times a free field algebra, while the latter embeds itself in a certain free field algebra, see [Ad19] for details. Note, that the Virasoro algebra is the principal W-algebra of sl 2 .…”
Section: Commutative Algebras Via Free Field Realizationsmentioning
confidence: 99%
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“…Also note that the connection between characters of modules is already quite interesting. For example in the simplest example of sl 2 at admissible level characters are formal distributions or expansions of meromorphic Jacobi forms [CR1,Ad5], while characters of the N = 2 super Virasoro algebra are expressed in terms of Jacobi theta functions and mock Jacobi forms [STT]. This correspondence has been studied in [FSST,S3,KoSa,CLRW].…”
Section: Introductionmentioning
confidence: 99%