Tuesday, May 19, 15:15, 7.527

Geetha Thangavelu (IISER Thiruvananthapuram), Mackey decomposition for the walled Brauer algebras.

Abstract:
In this talk, we establish a Mackey-type decomposition theorem for modules over walled Brauer algebras. Motivated by the classical Mackey decomposition theorem for finite groups, our work extends the diagram algebra framework developed by Hartmann for Brauer algebras. Using the cellularly stratified structure of the walled Brauer algebra, we define appropriate induction and restriction functors and derive a decomposition theorem for permutation modules. As an application, we obtain a decomposition formula for homomorphism spaces between permutation modules over walled Brauer algebras. I will also discuss our ongoing work on extensions of these methods to other diagram algebras and comment on their significance in understanding the associated Schur algebras.
This is joint work with my student, Bristi Chakraborty.