论文标题
离散的傅立叶变换，量子$ 6J $ -Symbols和深度截断的四面体
Discrete Fourier transforms, quantum $6j$-symbols and deeply truncated tetrahedra
论文作者
论文摘要
量子$ 6J $ -Symbols的渐近行为与截短的高中心四面体\，\ cite {C}的体积密切相关，并且在理解Turaev-Viro Inffortiants的渐近学方面起着核心作用。在本文中，我们提出了一个猜想，该猜想一方面是量子$ 6J $ -Symbols的离散傅立叶变换的渐近变换，另一方面是各种类型的深层截断的四面体。作为支持证据，我们证明了构想的情况：二面角足够小，并且在二面角相对较大的情况下提供了数值计算。一个关键的观察结果是量子$ 6J $ -Symbols与深截断的四面体的共同销售功能之间的关系，这本身就是很感兴趣的。更加雄心勃勃地，我们将猜想扩展到平面图的横向不变的离散傅立叶变换和深层截断的多面体的体积，并提供支持证据。
The asymptotic behavior of quantum $6j$-symbols is closely related to the volume of truncated hyperideal tetrahedra\,\cite{C}, and plays a central role in understanding the asymptotics of the Turaev-Viro invariants of $3$-manifolds. In this paper, we propose a conjecture relating the asymptotics of the discrete Fourier transforms of quantum $6j$-symbols on one hand, and the volume of deeply truncated tetrahedra of various types on the other. As supporting evidence, we prove the conjecture in the case that the dihedral angles are sufficiently small, and provide numerical calculations in the case that the dihedral angles are relatively big. A key observation is a relationship between quantum $6j$-symbols and the co-volume function of deeply truncated tetrahedra, which is of interest in its own right. More ambitiously, we extend the conjecture to the discrete Fourier transforms of the Yokota invariants of planar graphs and volume of deeply truncated polyhedra, and provide supporting evidence.
