On the classification of non-equal rank affine conformal embeddings and applications
Name
1702.06089.pdf
Description
Submitted version
Size
408 KB
Format
Adobe PDF
Checksum (MD5)
233253841342c08bb59119dda74b2a02
Author(s)
Adamović, Dražen
Kac, Victor G
Frajria, Pierluigi Möseneder
Papi, Paolo
Perše, Ozren
Date Issued
2018
Journal
Selecta Mathematica, New Series
Publisher
Springer Science and Business Media LLC
Version
Original manuscript
Abstract
© 2018, Springer International Publishing AG, part of Springer Nature. 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/S00029-017-0386-7
