Harder-Narasimhan Filtrations and Zigzag Persistence
Marc Fersztand, Vidit Nanda, Ulrike Tillmann
TL;DR
This paper establishes a connection between Harder-Narasimhan filtrations in sheaf theory and the barcode of periodic zigzag persistence modules for affine type quivers, advancing understanding in algebraic topology and representation theory.
Contribution
It introduces a sheaf-theoretic stability condition and links the Harder-Narasimhan filtration to zigzag persistence barcodes for affine quivers.
Findings
Harder-Narasimhan filtration corresponds to zigzag persistence barcode
Established a precise relationship for affine type $ ilde{A}$ quivers
Provides new tools for analyzing quiver representations
Abstract
We introduce a sheaf-theoretic stability condition for finite acyclic quivers. Our main result establishes that for representations of affine type 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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Quantum many-body systems · Topological and Geometric Data Analysis