A deterministic algorithm for Harder-Narasimhan filtrations for representations of acyclic quivers
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866909094553583616 |
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| author | Cheng, chi-yu |
| author_facet | Cheng, chi-yu |
| contents | 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 $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_06428 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A deterministic algorithm for Harder-Narasimhan filtrations for representations of acyclic quivers Cheng, chi-yu Representation Theory Algebraic Geometry 14Q20 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 $M$. |
| title | A deterministic algorithm for Harder-Narasimhan filtrations for representations of acyclic quivers |
| topic | Representation Theory Algebraic Geometry 14Q20 |
| url | https://arxiv.org/abs/2111.06428 |