Stability conditions and braid group actions on affine An quivers

Abstract

We study stability conditions on the Calabi–Yau-[Formula: see text] categories associated to an affine type [Formula: see text] quiver which can be constructed from certain meromorphic quadratic differentials with zeroes of order [Formula: see text]. We follow Ikeda’s work to show that this moduli space of quadratic differentials is isomorphic to the space of stability conditions quotient by the spherical subgroup of the autoequivalence group. We show that the spherical subgroup is isomorphic to the braid group of affine type [Formula: see text] based on the Khovanov–Seidel–Thomas method.