On the classification of non-equal rank affine conformal embeddings and applications

• Drazen Adamovíc ^[1] ; Victor G. Kac ^[4] ; Pierluigi Möseneder Frajria ^[2] ; Paolo Papi ^[3] ; Ozren Perse ^[1]
  1. [1] University of Zagreb

     University of Zagreb

     Croacia

     
  2. [2] Polytechnic University of Milan

     Polytechnic University of Milan

     Milán, Italia

     
  3. [3] Università de Roma La Sapienza

     Università de Roma La Sapienza

     Roma Capitale, Italia

     
  4. [4] Department of Mathematics

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 3, 2018, págs. 2455-2498
• Idioma: inglés
• DOI: 10.1007/s00029-017-0386-7
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• Resumen

  • We complete the classification of conformal embeddings of a maximally reductive subalgebra k into a simple Lie algebra g at non-integrable non-critical levels k by dealing with the case when k has rank less than that of g . We describe some remarkable instances of decomposition of the vertex algebra Vk(g) as a module for the vertex subalgebra generated by k . We discuss decompositions of conformal embeddings and constructions of new affine Howe dual pairs at negative levels. In particular, we study an example of conformal embeddings A1×A1↪C3 at level k=−1/2 , and obtain explicit branching rules by applying certain q-series identity. In the analysis of conformal embedding A1×D4↪C8 at level k=−1/2 we detect subsingular vectors which do not appear in the branching rules of the classical Howe dual pairs.