Colloquium abstracts

Digjoy Paul
September 23, 2021

Schur--Weyl dualities and Partition algebras:  In 1905 Schur developed the polynomial representation theory of the general linear group over the field of complex numbers. He considered its natural action on a tensor space on which symmetric group also acts naturally. These commuting actions lead Schur to transfer information about the representation theory of the Symmetric group to the general linear group and vice versa. Over the decades, this remarkable connection, popular as Schur--Weyl duality, has been generalised for various pairs of groups/algebras. Motivated by the Potts model in statistical mechanics, Jones and Martin restricted the action of the general linear group to the permutation matrices sitting inside it, and they discovered the so-called Partition algebra. We shall briefly discuss reasons why mathematicians have been interested in partition algebra. We conclude the talk by introducing a generalisation of partition algebra, joint work with Narayanan and Srivastava.