Duality and Combinatorics of Long Strings in ADS3

The counting of long strings in ADS3, in the context of Type IIB string theory on $AD{S}_3\times S^3\times T^4$, is used to exhibit the action of the duality group $O(5,5;Z)$, and in particular its Weyl Subgroup $S_5 \bowtie Z_2$, in the non-perturbative phenomena associated with continuous spectra of states in these backgrounds. The counting functions are related to states in Fock spaces. The symmetry groups also appear in the structure of compactifications of instanton moduli spaces on $T^4$.