Chennai Mathematical Institute


3:30 pm, Seminar Hall
Schur-Weyl duality, diagram algebras and cellular algebras

T. Geetha
Chennai Mathematical Institute.


Schur-Weyl duality is the foundational result in representation theory which connects the representation theory of general linear groups and the symmetric groups. It's 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 of general linear group. After Schur's work, several attempts have been made to study the analogues of this duality. We will explore two important class of algebras called "Schur algebras" and "diagram algebras" which arise from this duality in connection to other theories like Lie theory, quantum groups, statistical mechanics and mathematical physics. In this talk we will see an overview of these algebras, the theory of cellular algebras introduced by Graham and Lehrer (1996)) which provides a beautiful model to understand these class of algebras and my recent work in this direction.