AI 中文总结
研究 A 型施普林格表示在完全旗簇同调中的几何实现，通过斯佩特多项式等进行一系列正展开，解决两行纤维的施普林格问题，证明相关猜想并识别施普林格基与网基，还推导了旗簇泊松退化轨迹分量的舒伯特圈展开。
AI 中文摘要
我们证明了 A 型施普林格表示在完全旗簇的同调中由斯佩特多项式几何地实现。对于任何划分，我们将斯佩特模的经典斯佩特多项式生成元与一族不相交的列维 - 理查森簇的类进行了识别，并且这一族簇退化为相应的施普林格纤维。这通过一系列正展开，从斯佩特多项式经约瑟夫多项式到舒伯特圈，将施普林格纤维分量的舒伯特正性问题进行了分解。对于两行划分，我们使这些展开在组合上明确，给出了列维 - 理查森圈和施普林格纤维分量的明显非负舒伯特圈展开。这解决了两行纤维的施普林格问题，证明了普雷库普和萨班多 - 阿尔瓦雷斯的两个猜想，并将施普林格基与两行斯佩特模的网基进行了识别。作为应用，我们推导了旗簇的泊松退化轨迹分量的舒伯特圈展开。
英文摘要
We show that the type A Springer representation is realized geometrically in the homology of the complete flag variety by Specht polynomials. For any partition, we identify the classical Specht polynomial generators of the Specht module with the classes of a family of disjoint Levi--Richardson varieties, and this family degenerates to the corresponding Springer fiber. This factors Springer's Schubert positivity problem for Springer fiber components through a chain of positive expansions, from Specht polynomials through the Joseph polynomials to the Schubert cycles. For two-row partitions we make each of these expansions combinatorially explicit, giving manifestly nonnegative Schubert cycle expansions of both the Levi-Richardson cycles and the Springer fiber components. This resolves Springer's question for two-row fibers and proves two conjectures of Precup and Sabando-Alvarez, and identifies the Springer basis with the web basis for two-row Specht modules. As an application, we deduce the Schubert cycle expansions of the components of the Poisson degeneracy locus of the flag variety.
Comments29 pages, comments welcome!
