FERMIONIC QUASI-PARTICLE REPRESENTATIONS FOR CHARACTERS OF (G(1))1X(G(1))1 (G(1))2/

We present fermionic quasi-particle sum representations for some of th e characters (or branching functions) of (G(1))1 X (G(1))1/(G(1))2 for all simply-laced Lie algebras G. For given G the characters are writt en as the partition function of a set of rank G types of massless quas i-particles in certain charge sectors, with nontrivial lower bounds on the one-particle momenta. We discuss the non-uniqueness of the repres entation for the identity character of the critical Ising model, which arises in both the A1 and E8 cases.