论文标题
鲁滨逊 - 施加对应的部分排列
A Robinson-Schensted Correspondence for Partial Permutations
论文作者
论文摘要
我们研究了与矩阵Schubert品种相关的Steinberg品种，并开发了Robinson-Schensted类型对应关系，$τ\ leftrightArrow（λ，\ Mathsf Q，\ Mathsf P）$。这里的$τ$是大小$ p \ times q $，$λ$的部分排列，可允许的签名的年轻图$ $ p+q $，$ \ \ \ \ \ m rathsf p $（resp。$ \ $ \ \ \ \ \ \ \ \ \ \ \ \ \ \ mathsf q $）是$ p $ $ p $ $ p $ $ p $ $λ$的标准的年轻tableau（resp。$ q $）。通过将Matrix Schubert品种嵌入Schubert品种中，我们发现了经典的Robinson-Schensted-Knuth对应关系与我们的两者之间的密切关系。我们还表明，$（λ，\ Mathsf Q，\ Mathsf P）\ mapsto（λ^\ vee，\ Mathsf P，\ Mathsf Q）$对应于Matrix Schubert品种上的投影二元性。
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 also show that an involution $(Λ,\mathsf Q,\mathsf P)\mapsto(Λ^\vee,\mathsf P,\mathsf Q)$ corresponds to projective duality on matrix Schubert varieties.
