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A deterministic algorithm for Harder–Narasimhan filtrations for representations of acyclic quivers

Chi-Yu Cheng

Vol. 18 (2024), No. 2, 319–347
DOI: 10.2140/ant.2024.18.319

Let M be a representation of an acyclic quiver Q over an infinite field k. We establish a deterministic algorithm for computing the Harder–Narasimhan filtration of M. The algorithm is polynomial in the dimensions of M, the weights that induce the Harder–Narasimhan filtration of M, and the number of paths in Q. As a direct application, we also show that when k is algebraically closed and when M is unstable, the same algorithm produces Kempf’s maximally destabilizing one parameter subgroups for M.

geometric invariant theory, weight stability, slope stability, representation, quiver, Harder–Narasimhan filtration, discrepancy
Mathematical Subject Classification
Primary: 14L24, 14Q20, 16G20
Received: 24 June 2022
Revised: 16 January 2023
Accepted: 20 March 2023
Published: 6 February 2024
Chi-Yu Cheng
University of Missouri
Columbia, MO
United States

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