Exact Lagrangian fillings of twist-spun torus links

In this paper, we construct exact Lagrangian fillings of Legendrian torus links [Formula: see text] that are fixed by a Legendrian loop that acts by [Formula: see text] rotation. By using these rotationally symmetric fillings, we produce fillings of the corresponding Legendrian twist-spun tori. Our construction is combinatorial in nature, relating symmetric weakly separated collections and plabic graphs to symmetric Legendrian weaves via the T-shift procedure of Casals, Le, Sherman–Bennett, and Weng. The main technical ingredient in this process is a necessary and sufficient condition for the existence of maximal weakly separated collections of [Formula: see text]-element subsets of [Formula: see text] that are fixed by addition of [Formula: see text] modulo [Formula: see text].