Stability conditions and braid group actions on affine $A_n$ quivers

Abstract

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 Khovanov-Seidel-Thomas method.

A Frobenius manifold for $\ell$-Kronecker quiver

“…Namely, in [BQS14,HKK17] (resp. [Ike14,Ike17,Wan19]), their central charges are given by the oscillatory integrals (resp. period integrals of Gelfand-Leray forms) for primitive forms and the spaces of stability conditions are isomorphic to the (resp.…”