部分旗簇几何中的Robinson-Schensted-Knuth对应

部分标志的经典和奇异Robinson-Schensted-Knuth对应

Classic and mirabolic Robinson-Schensted-Knuth correspondence for partial flags

在本文中，我们首先推广到部分标志的情况下，证明了由Spalberth和Steinberg的结果，涉及到两个完整的标志和不可约的组成部分的相对位置的标志品种，他们的谎言，使用Robinson-Schensted-Knuth对应。然后，我们使用这个结果推广的Mirabolic Robinson-Schensted-Knuth对应定义的Travkin，两个部分标志和一条线的情况下。

A Robinson-Schensted Correspondence for Partial Permutations

We study the Steinberg variety associated to matrix Schubert varieties, and develop a Robinson-Schensted type correspondence, $τ\leftrightarrow(Λ,\mathsf Q,\mathsf P)$. Here $τ$ is a partial permutation of size $p\times q$, $Λ$ an admissible signed Young diagram of size $p+q$, and $\mathsf P$ (resp. $\mathsf Q$) a standard Young tableau of size $p$ (resp. $q$) whose shape is determined by $Λ$. By embedding the matrix Schubert variety into a Schubert variety, we find a close relationship between the combinatorics of the classical Robinson-Schensted-Knuth correspondence and our bijection. We als…

有界Robinson-Schensted-Knuth对应下Grassmannian Richardson簇的局部性质

Local Properties of Richardson Varieties in the Grassmannian via a Bounded Robinson-Schensted-Knuth Correspondence

本文给出了Grassmannian中Richardson簇的切锥理想在任意T-不动点处的显式Grobner基，从而推广了Kodiyalam-Raghavan和Kreiman-Lakshmibai的一个结果.我们的证明是基于广义的Robinson-Schensted-Knuth（RSK）对应，我们称之为有界RSK（BRSK）。利用Grobner基的结果，通过对不相交格路族的计数，导出了Richardson簇在任意T-不动点的重数公式，推广了Krattehthaler首先证明的一个结果.

Mirabolic Robinson-Schensted-Knuth correspondence

The set of orbits of $GL(V)$ in $Fl(V)\times Fl(V)\times V$ is finite, and is parametrized by the set of certain decorated permutations in a work of Solomon. We describe a Mirabolic RSK correspondence (bijective) between this set of decorated permutations and the set of triples: a pair of standard Young tableaux, and an extra partition. It gives rise to a partition of the set of orbits into combinatorial cells. We prove that the same partition is given by the type of a general conormal vector to an orbit. We conjecture that the same partition is given by the bimodule Kazhdan-Lusztig cells in t…

奇异Spaltenstein簇

Exotic Spaltenstein varieties

本文定义奇异Spaltenstein簇以推广经典Spaltenstein簇，证明二阶自伴幂零自同态情形下最高维不可约分量与半标准Young双表一一对应，并给出最高维数的组合公式。

正交Grassmannian中Richardson簇的切锥的初始理想的有界RSK对应

Initial ideals of tangent cones to Richardson varieties in the Orthogonal Grassmannian via a Orthogonal-Bounded-RSK-Correspondence

正交格拉斯曼中的Richardson簇$X_\ga^\gc$被定义为正交格拉斯曼中的舒伯特簇$X^\gc$与其中的相反舒伯特簇$X_\ga$的交集。给出了$X_\ga^\gc$的任意$T$ -不动点处切锥理想的初始理想（关于某些方便选择的项阶）的显式描述，从而推广了Raghavan-Upadhyay \cite{Ra-Up2}的一个结果.我们的证明是基于广义的Robinson-Schensted-Knuth（RSK）对应，我们称之为正交有界RSK（OBRSK）。OBRSK对应将给出由切锥的理想的初始理想（如上所述）定义的一组单项式和“标准单项式基”之间的保度双射。Kreiman在\cite{Kr-bkrs}中对普通Grassmannian中的Richardson变种做了类似的工作。