  A 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.
