Generalized Rogers Ramanujan Expressions for Some Non--Singlet Twisted Affine Algebras

TL;DR

This paper extends generalized Rogers-Ramanujan expressions to non-singlet string functions of twisted affine algebras, providing explicit formulas and verification methods for these mathematical objects.

Contribution

It introduces new GRR expressions for non-singlet string functions of twisted affine algebras, including a complete set for A2^{(2)}.

Findings

Derived explicit GRR formulas for non-singlet string functions.

Verified formulas using Freudenthal--Kac formula.

Extended known results from singlet to non-singlet cases.

Abstract

Hatayama et al. described generalized Rogers--Ramanujan (GRR) expressions for the string functions of the singlet representation of twisted affine algebras. We give here such GRR expressions for some non-singlet string functions. In the case of the algebra $A_2^{(2)}$ this gives all the string functions. We verify these expressions using Freudenthal--Kac formula.