Stability conditions for affine type A

Abstract

We construct maximal green sequences of maximal length for any affine quiver of type $A$. We determine which sets of modules (equivalently $c$-vectors) can occur in such sequences and, among these, which are given by a linear stability condition (also called a central charge). There is always at least one such maximal set which is linear. The proofs use representation theory and three kinds of diagrams shown in Figure 1. Background material is reviewed with details presented in two separate papers [arxiv:1706.06986] and [arXiv:1706.06503].