We study stability conditions on the Calabi-Yau-N categories associated to an affine type An quiver which can be constructed from certain meromorphic quadratic differentials with zeroes of order N-2. 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 A based on the Khovanov-Seidel-Thomas method.
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