2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/203412A class of mathematical dualities have played a central role in mapping states in gauge theory to states in the spacetime string theory dual. This includes the classical Schur-Weyl duality between symmetric groups and Unitary groups, as well as generalisations involving Brauer and Hecke algebras. The physical string dualities involved include examples from the AdS/CFT correspondence as well as the string dual of two-dimensional Yang Mills.10 pages,talk given at ``Ten years of AdS/CFT,'' Buenos Aires, December 19-21, 2007High Energy Physics - TheoryRepresentation Theorytext