On multi-color partitions and the generalized Rogers-Ramanujan identities

Basil Gordon, in the sixties, and George Andrews, in the seventies, general ized the Rogers-Ramanujan identities to higher moduli. These identities ari se in many areas of mathematics and mathematical physics. One of these area s is representation theory of infinite dimensional Lie algebras, where vari ous known interpretations of these identities have led to interesting appli cations. Motivated by their connections with Lie algebra representation the ory, we give a new interpretation of a sum related to generalized Rogers-Ra manujan identities in terms of multi-color partitions.