Grassmannian braiding categorified

In 2017, Chris Fraser discovered an action of the extended affine braid group on d strands on the Grassmannian of k-subspaces in n-space, endowed with its cluster structure due to Scott (2006). Here, the integer d stands for the greatest common divisor of k and n. In joint work with Fraser and Haoyu Wang, we construct a categorical lift of this action using Jensen-King-Su's (additive) categorification of the Grassmannian via Cohen-Macaulay modules over a singular quotient of the preprojective algebra P of extended type A_{n-1}. A key ingredient is Seidel-Thomas' braid group action (2000) on the derived category of P.