Fermionic Quasi-Particle Representations for Characters of $(G^{(1)}{)}_1\times (G^{(1)}{)}_1ø(G^{(1)}{)}_2$

Abstract

We present fermionic quasi-particle sum representations for some of the characters (or branching functions) of ~$(G^{(1)}{)}_1\times (G^{(1)}{)}_1ø(G^{(1)}{)}_2$ ~for all simply-laced Lie algebras $G$. For given $G$ the characters 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 representations for the identity character of the critical Ising model, which arises in both the $A_1$ and $E_8$ cases.

14/9 pages in harvmac, ITP-SB-92-64/RU-92-51. References added