Parafermionic bases of standard modules for affine Lie algebras

Abstract

In this paper we construct combinatorial bases of parafermionic spaces associated with the standard modules of the rectangular highest weights for the untwisted affine Lie algebras. Our construction is a modification of G. Georgiev’s construction for the affine Lie algebra \({\widehat{\mathfrak {s}l}}(n+1,\mathbb C)\)—the constructed parafermionic bases are projections of the quasi-particle bases of the principal subspaces, obtained previously in a series of papers by the first two authors. As a consequence we prove the character formula of A. Kuniba, T. Nakanishi and J. Suzuki for all non-simply-laced untwisted affine Lie algebras.

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Acknowledgements

The authors would like to express their sincere gratitude to the anonymous referee for careful reading and many valuable comments and suggestions which helped them to improve the manuscript. This work has been supported in part by Croatian Science Foundation under the project UIP-2019-04-8488. The first and the third author are partially supported by the QuantiXLie Centre of Excellence, a project cofinanced by the Croatian Government and European Union through the European Regional Development Fund - the Competitiveness and Cohesion Operational Programme (Grant KK.01.1.1.01.0004).

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Correspondence to Slaven Kožić.

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Butorac, M., Kožić, S. & Primc, M. Parafermionic bases of standard modules for affine Lie algebras. Math. Z. (2020). https://doi.org/10.1007/s00209-020-02639-w

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Keywords

  • Affine Lie algebras
  • Parafermionic space
  • Combinatorial bases

Mathematics Subject Classification

  • Primary 17B67
  • Secondary 17B69
  • 05A19