The AdS/CFT correspondence and spectrum generating algebras

We list the spectrum generating algebras for string theory and M-theory compactified on various backgrounds of the form AdS_d+1 × Sⁿ. We identify the representations of these algebras which make up the classical supergravity spectra and argue for the presence of these spectrum generating algebras in the classical string/M-theory. We alsogt discuss the role of the spectrum generating algebras on the conformal field theory side.