Ringel duality for perverse sheaves on hypertoric varieties

Abstract

Motivated by the polynomial representation theory of the general linear group and the theory of symplectic singularities, we study a category of perverse sheaves with coefficients in a field k on any affine unimodular hypertoric variety M. Our main result is that this is a highest weight category whose Ringel dual is the corresponding category for the Gale dual hypertoric variety M!. On the way to proving our main result, we confirm a conjecture of Finkelberg–Kubrak in the case of hypertoric varieties. We also show that our category is equivalent to representations of a combinatorially-defined algebra, recently introduced in a related paper.