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Harder-Narasimhan Filtrations and Zigzag Persistence (2211.07553v2)
Published 14 Nov 2022 in math.RT and math.AT
Abstract: We introduce a sheaf-theoretic stability condition for finite acyclic quivers. Our main result establishes that for representations of affine type $\widetilde{\mathbb{A}}$ quivers, there is a precise relationship between the associated Harder-Narasimhan filtration and the barcode of the periodic zigzag persistence module obtained by unwinding the underlying quiver.
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