论文标题
NAHM总和，Quiver结果和K理论状况的组合学
Combinatorics of Nahm sums, quiver resultants and the K-theoretic condition
论文作者
论文摘要
本文中考虑的代数nahm方程是多项式方程，管理$ q \ rightarrow 1 $ $ q $ - hyphemementric nahm sums的限制。他们出现在各种领域：双曲几何，结理论，颤抖的代表理论，拓扑字符串和保形场理论。在本文中，我们主要集中于与对称颤动有关的NAHM总和和NAHM方程。对于其中的一大批，我们证明了颤抖的a polynomials（NAHM方程的专门结果）是矫正的（所谓的K理论条件）。这意味着它们是可量化的。此外，我们发现他们的脸多项式遵守了一个显着的组合模式。我们使用初始形式和混合多面体分解的机械来研究牛顿多层人群的边缘。我们表明，这种条件适用于具有邻接矩阵$ C = \ mathrm {diag}（α，α，α，\ dots，α），\α\ geq 2 $的对角颤动，并提供了几款非二元格式Quivers的检查。我们的猜想是，K理论条件适用于所有对称箭丝。
Algebraic Nahm equations, considered in the paper, are polynomial equations, governing the $q\rightarrow 1$ limit of the $q$-hypergeometric Nahm sums. They make an appearance in various fields: hyperbolic geometry, knot theory, quiver representation theory, topological strings and conformal field theory. In this paper we focus primarily on Nahm sums and Nahm equations that arise in relation with symmetric quivers. For a large class of them, we prove that quiver A-polynomials -- specialized resultants of the Nahm equations, are tempered (the so-called K-theoretic condition). This implies that they are quantizable. Moreover, we find that their face polynomials obey a remarkable combinatorial pattern. We use the machinery of initial forms and mixed polyhedral decompositions to investigate the edges of the Newton polytope. We show that this condition holds for the diagonal quivers with adjacency matrix $C = \mathrm{diag}(α,α,\dots,α),\ α\geq 2$, and provide several checks for non-diagonal quivers. Our conjecture is that the K-theoretic condition holds for all symmetric quivers.
