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.

30 pages, minor changes and corrections

References in corpus (2)

• Level Two String Functions and Rogers Ramanujan Type Identities
• On The Characters of Parafermionic Field Theories

Cited by in corpus (2)

• Combinatorial bases of standard modules of twisted affine Lie algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$: rectangular highest weights
• Generalized Rogers Ramanujan Expressions for Some Non--Singlet Twisted Affine Algebras