Generalized Rogers Ramanujan Identities for Twisted Affine Algebras

TL;DR

This paper verifies conjectured Rogers Ramanujan type identities for string functions of twisted affine Lie algebras using Lie algebraic methods, confirming their validity at low ranks and levels.

Contribution

It provides a computational verification of Hatayama et al.'s conjectures for twisted affine algebra string functions, extending known identities to twisted cases.

Findings

Confirmed the conjectured identities for all low-rank, low-level cases

Used Lie algebraic methods and Freudenthal's formula for verification

Achieved complete agreement with the conjectures

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 twisted affine Lie algebras. Conjectures 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.