Generalized Rogers–Ramanujan identities for twisted affine algebras

Abstract

The characters of parafermionic conformal field theories are given by the string functions of affine algebras, which are either twisted or untwisted algebras. Expressions for these characters as generalized Rogers–Ramanujan algebras have been established for the untwisted affine algebras. However, we study the identities for the string functions of the twisted affine Lie algebras. A conjecture for the string functions was proposed by Hatayama et al., for the unit fields, which expresses the string functions as Rogers–Ramanujan type sums. Here we propose to check the Hatayama et al. conjecture, using Lie algebraic theoretic methods. We use Freudenthal’s formula, which we computerized, to verify the identities for all the algebras at low rank and low level. We find complete agreement with the conjecture.