论文标题
新的高量子通风结构作为$ \ mathcal {w}的模块（\ mathfrak {gl} _r）$ - 代数
A New Class of Higher Quantum Airy Structures as Modules of $\mathcal{W}(\mathfrak{gl}_r)$-Algebras
论文作者
论文摘要
量子$ r $ - airy结构可以作为$ \ mathcal {w}的模块构建（\ mathfrak {gl} _r）$ - 代数通过限制基础海森伯格代数的扭曲模块。在本文中，我们对所有这些更高的量子通风结构进行了分类，这些结构是由由cartan subemalgebra的自动形态扭曲的模块产生的，这些结构由相同长度的分离周期的产物组成。这些较高的量子通风结构的一个有趣特征是必须仔细选择DILATON移位以满足矩阵的可逆性条件，而自然的选择是统一的根源。我们探讨了这些较高的量子通风结构如何为可减少的代数光谱曲线提供Chekhov，Eynard和Orantin拓扑递归的定义。我们还研究了从哪些条件下，通过任意自构扭曲的模块产生的量子$ r $ r $ airy结构可以扩展到新的量子$（r+1）$ - 通风的结构，而无需更改dilaton偏移而将琐碎的单周期添加到扭曲中。
Quantum $r$-Airy structures can be constructed as modules of $\mathcal{W}(\mathfrak{gl}_r)$-algebras via restriction of twisted modules for the underlying Heisenberg algebra. In this paper we classify all such higher quantum Airy structures that arise from modules twisted by automorphisms of the Cartan subalgebra consisting of products of disjoint cycles of the same length. An interesting feature of these higher quantum Airy structures is that the dilaton shifts must be chosen carefully to satisfy a matrix invertibility condition, with a natural choice being roots of unity. We explore how these higher quantum Airy structures may provide a definition of the Chekhov, Eynard, and Orantin topological recursion for reducible algebraic spectral curves. We also study under which conditions quantum $r$-Airy structures that come from modules twisted by arbitrary automorphisms can be extended to new quantum $(r+1)$-Airy structures by appending a trivial one-cycle to the twist without changing the dilaton shifts.
