Symplectic higher Auslander correspondence for type A

Abstract

We prove that the Fukaya–Seidel categories of a certain family of singularities on ${\mathbb{C}}^d$ are equivalent to the perfect derived categories of higher Auslander algebras of Dynkin type A. We relate these to the Fukaya–Seidel categories of Brieskorn–Pham singularities and to the partially wrapped Fukaya categories considered by Dyckerhoff–Jasso–Lekili. We provide a symplectic interpretation to higher Auslander correspondence of type A in terms of Fukaya–Seidel categories of Lefschetz fibrations.