Fermionic quasi-particle representations for characters of (G (1) ) 1 × (G (1) ) 1 /(G (1) ) 2

Abstract We present fermionic quasi-particle sum representations for some of the characters (or branching functions) of ( G (1) ) 1 × ( G (1) ) 1 ( G (1) ) 2 for all simply-laced Lie algebras G. For given G the charactters are written as the partition function of a set of rank G types of massless quasi-particles in certain charge sectors, with nontrivial lower bounds on the one-particle momenta. We discuss the non-uniqueness of the representation for the identity character of the critical Ising model, which arises in both the A 1 and E 8 cases.