Higher-order congruence relations on affine moment graphs: The subgeneric case

Abstract

We study the structure algebra Z of the stable moment graph for the case of the affine root system A1. The structure algebra Z is an algebra over a symmetric algebra and in particular, it is a module over a symmetric algebra. We study this module structure on Z and we construct a basis. By “setting c equal to zero” in Z, we obtain the module Zc=0. This module can be described in terms of the finite root system A1 and we show that it is determined by a set of certain divisibility relations. These relations can be regarded as a generalization of ordinary moment graph relations that define sections of sheaves on moment graphs, and because of this we call them higher-order congruence relations.