  A GRR expression for the characters of $A$-type parafermions has been a long
standing puzzle dating back to conjectures made regarding some of the
characters in the 80's. Not long ago we have put forward such GRR type
identities describing any of the level two $ADE$-type generalized parafermions
characters at any rank. These characters are the string functions of simply
laced Lie algebras at level two as such they are also of mathematical interest.
In our last joint paper we presented the complete derivation for the $D$-type
generalized parafermions characters identities. Here we generalize our previous
discussion and prove the GRR type expressions for the characters of $A$-type
generalized parafermions. To prove the $A$-type GRR conjecture we further our
study of $q$-diagrams, introduced in our last joint paper, and examine the
diagrammatic interpretations of known identities among them Slater identities
for the characters of the first minimal model and the Bailey lemma.
