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 $\widehat{\mathfrak sl}(n+1,\mathbb C)$the constructed parafermionic bases are projections of the quasiparticle 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 nonsimplylaced untwisted affine Lie algebras.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.00435
 Bibcode:
 2020arXiv200200435B
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory;
 Mathematics  Representation Theory;
 17B67 (Primary) 17B69;
 05A19 (Secondary)
 EPrint:
 30 pages, minor changes and corrections