Abstract :

Schur-Weyl duality is the foundational result in representation theory which connects the representation theory of general linear groups and the symmetric groups. Its classical version due to Issai Schur (1901 and 1927) can be viewed as an another formulation of first and second fundamental theorem of invariant theory for general linear group. After Schur's work several attempts have been made to study the analogues of this duality. In this talk we will see an important class of diagram algebras arising from this duality in connection to Lie theory, quantum groups and statistical mechanics and my recent work in this direction.