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Symmetry Principles for String Theory

The gauge symmetries that underlie string theory arise from inner automorphisms of the algebra of observables of the associated conformal field theory. In this way it is possible to study broken and unbroken symmetries on the same footing, and exhibit an infinite-dimensional supersymmetry algebra that includes space-time diffeomorphisms and an infinite number of spontaneously broken level-mixing symmetries. We review progress in this area, culminating in the identification of a weighted tensor algebra as a subalgebra of the full symmetry. We also briefly describe outstanding problems. Talk presented at the Gursey memorial conference, Istanbul, Turkey, June, 1994.