论文标题
通风的理想，转向和$ \ Mathcal {w}（\ Mathfrak {sp} _ {2n}）$ - 代数
Airy ideals, transvections and $\mathcal{W}(\mathfrak{sp}_{2N})$-algebras
论文作者
论文摘要
在本文的第一部分中，我们提出了关于较高通风结构（或通风理想）理论的不同观点，该理论可能会揭示其起源。我们在REES Weyl代数的$ \ hbar $ -ADIC完成中定义了通风的理想，并表明将通风的理想定义为精确的定义，使它们始终与由Rees Weyl代数的自动形态产生的衍生物产生的规范左左理想相关，我们呼叫转移。然后，标准的存在和独特性导致通风结构理论立即遵循。 在本文的第二部分中，我们构建了由$ \ Mathfrak {sp} _ {sp} _ {2n} $在级别$ n-1/2 $上的$ \ mathfrak {sp} _ {2n} $ of $ n-1/2 $的强$ \ Mathcal W $ -Algebra的非负模式产生的通风理想。这提供了海森堡代数中通风理想的示例，该示例需要将零模式视为衍生物而不是变量，这导致了对所得分区功能的有趣解释。
In the first part of the paper we propose a different viewpoint on the theory of higher Airy structures (or Airy ideals) which may shed light on its origin. We define Airy ideals in the $\hbar$-adic completion of the Rees Weyl algebra, and show that Airy ideals are defined exactly such that they are always related to the canonical left ideal generated by derivatives by automorphisms of the Rees Weyl algebra of a simple type, which we call transvections. The standard existence and uniqueness result in the theory of Airy structures then follows immediately. In the second part of the paper we construct Airy ideals generated by the non-negative modes of the strong generators of the principal $\mathcal W$-algebra of $\mathfrak{sp}_{2N}$ at level $N-1/2$, following the approach developed in arXiv:1812.08738. This provides an example of an Airy ideal in the Heisenberg algebra that requires realizing the zero modes as derivatives instead of variables, which leads to an interesting interpretation for the resulting partition function.
