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

Volume 18
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

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
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
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

Algebra & Number Theory is part of our Subscribe to Open program. The decision whether this article will be published Open Access will be made soon. To help make this possible, please encourage your institution to subscribe.