Download this article
Download this article For screen
For printing
Recent Issues

Volume 19, 1 issue

Volume 18, 12 issues

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
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
Abstract

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.

Keywords
geometric invariant theory, weight stability, slope stability, representation, quiver, Harder–Narasimhan filtration, discrepancy
Mathematical Subject Classification
Primary: 14L24, 14Q20, 16G20
Milestones
Received: 24 June 2022
Revised: 16 January 2023
Accepted: 20 March 2023
Published: 6 February 2024
Authors
Chi-Yu Cheng
University of Missouri
Columbia, MO
United States
© 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

Open Access made possible by participating institutions via Subscribe to Open.