AI 中文总结
研究利用基本单极子算子构造卡茨 - 穆迪仿射格拉斯曼切片闭嵌入，通过特定 BFN 构造变体实现量子化，进而构造极限量子化 zastava 及其正部，证明其希尔伯特级数与卡茨多项式相关，还证明了内古特猜想。
AI 中文摘要
我们之前利用基本单极子算子构造了卡茨 - 穆迪仿射格拉斯曼切片的闭嵌入。这些空间通过箭图规范理论的库仑分支的布拉弗曼 - 芬克尔伯格 - 中岛构造来定义，一般情况下嵌入不量子化。然而，存在一种产生 zastava 空间的 BFN 构造变体，我们证明在这种情况下闭嵌入可量子化。这使我们能够取极限并为任意箭图构造极限量子化 zastava $\mathcal{A}$，该代数起博雷尔杨代数的作用。我们还构造了正部 $\mathcal{A}^+$，它起幂幺杨代数的作用。通过取单极子公式的极限，我们表明 $\mathcal{A}$ 和 $\mathcal{A}^+$ 的希尔伯特级数由卡茨多项式的华氏公式的一个版本给出。我们还表明 $\mathcal{A}^+$ 同构于某个洗牌代数。最后，利用这些结果，通过第二作者关于库仑分支生成元的工作，我们得到了关于局部洗牌代数的球面生成的内古特猜想的证明。
英文摘要
We previously constructed closed embeddings of Kac-Moody affine Grassmannian slices using fundamental monopole operators. These spaces are defined via the Braverman-Finkelberg-Nakajima construction of Coulomb branches for quiver gauge theories, and the embeddings do not quantize in general. However, there is variant of the BFN construction that produces zastava spaces, and we show that the closed embeddings do quantize in that case. This allows us to take a limit and construct the limit quantized zastava $\mathcal{A}$ for an arbitrary quiver. This algebra plays the role of the Borel Yangian. We also construct a positive part $\mathcal{A}^+$, which plays the role of the unipotent Yangian. By taking the limit of the monopole formula, we show that both $\mathcal{A}$ and $\mathcal{A}^+$ have Hilbert series given by a version for Hua's formula for Kac polynomials. We also show that $\mathcal{A}^+$ is isomorphic to a certain shuffle algebra. Finally, using these results we obtain a proof of Negut's conjecture on the spherical generation of localized shuffle algebras via the second author's work on generators of Coulomb branches.
Comments47 pages, comments welcome
