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 $M$.

中文翻译：

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用于表示非循环颤动的 Harder-Narasimhan 过滤的确定性算法

让$\mathrm{中号}$是非循环颤动的表示$问$在无限的领域$k$。我们建立了一种确定性算法来计算 Harder-Narasimhan 过滤$\mathrm{中号}$。该算法是维度为的多项式$\mathrm{中号}$，引起 Harder-Narasimhan 过滤的权重$\mathrm{中号}$，以及路径数$问$。作为直接应用，我们还表明，当$k$是代数封闭的并且当$\mathrm{中号}$是不稳定的，相同的算法产生 Kempf 的最大不稳定的一个参数子组$\mathrm{中号}$。