U-duality multiplets and non-perturbative superstring states

We employ an algebraic approach for unifying perturbative and non-perturbative superstring states on an equal footing, in the form of U-duality multiplets, at all excited string levels. In compactified type-IIA supertring theory we present evidence that the multiplet is labelled by two spaces, ``index'' space and ``base'' space, on which U acts without mixing them. Both spaces are non-perturbative extensions of similar spaces that label perturbative T-duality multiplets. Base space consists of all the central charges of the 11D SUSY algebra, while index space corresponds to represetations of the maximal compact subgroup K in U. This structure predicts the quantum numbers of the non-perturbative states. We also discuss whether and how U-multiplets may coexist with 11-dimensional multiplets, that are associated with an additional non-perturbative 11D structure that seems to be lurking behind in the underlying theory.