论文标题
Zonotopal代数，轨道谐波和对称震颤的Donaldson-Thomas不变性
Zonotopal algebras, orbit harmonics, and Donaldson-Thomas invariants of symmetric quivers
论文作者
论文摘要
我们将轨道谐波的方法应用于图表上的一组断裂分隔线和可定向的分隔线，以分别获得中央和外部的分层代数。然后，我们将Efimov在共同体厅代数的背景下与图形$ g_ {q，γ} $的中央Zonotopal代数相关联，该代数是由具有足够环的对称颤动$ Q $构建的，并具有足够的回路和尺寸vector $γ$。这为以前的作品提供了具体的组合观点，使我们能够将量子唐纳森 - 托马斯不变性识别为$s_γ$ -invariants的希尔伯特系列，该系列的nikov-shapiro Slim Slim Slim Slim Sliem graph Space of $ G_ {Q，γ} $。反过来，与轨道谐波的联系使我们能够向数值唐纳森 - 托马斯不变式提供明显的非负组合解释，因为$ g_ {q，γ，γ} $的$s_γ$ -ORBITS的数量是$s_γ$ -ORBITS的数量。我们以几种表示理论后果结束，其组合后果可能具有独立的利益。
We apply the method of orbit harmonics to the set of break divisors and orientable divisors on graphs to obtain the central and external zonotopal algebras respectively. We then relate a construction of Efimov in the context of cohomological Hall algebras to the central zonotopal algebra of a graph $G_{Q,γ}$ constructed from a symmetric quiver $Q$ with enough loops and a dimension vector $γ$. This provides a concrete combinatorial perspective on the former work, allowing us to identify the quantum Donaldson-Thomas invariants as the Hilbert series of the space of $S_γ$-invariants of the Postnikov-Shapiro slim subgraph space attached to $G_{Q,γ}$. The connection with orbit harmonics in turn allows us to give a manifestly nonnegative combinatorial interpretation to numerical Donaldson-Thomas invariants as the number of $S_γ$-orbits under the permutation action on the set of break divisors on $G_{Q,γ}$. We conclude with several representation-theoretic consequences, whose combinatorial ramifications may be of independent interest.
