Strands algebras and the affine highest weight property for equivariant hypertoric categories

We show that the equivariant hypertoric convolution algebras introduced by Braden–Licata–Proudfoot–Webster are affine quasi hereditary in the sense of Kleshchev and compute the Ext groups between standard modules. Together with the main result of [27], this implies a number of new homological results about the bordered Floer algebras of Ozsváth–Szabó, including the existence of standard modules over these algebras. We prove that the Ext groups between standard modules are isomorphic to the homology of a variant of the Lipshitz–Ozsváth–Thurston bordered strands dg algebras.