2017/09/09 by Braden, Tom, Mautner, Carl
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1709.03004
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. Our main result is that this is a highest weight category whose Ringel dual is the corresponding category for the Gale dual hypertoric variety. 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.