AI 中文总结
本文推广Worley-Sagan插入和Haiman混合插入至着色排列，保持对偶性，通过嵌入Shimozono-White双重混合插入证明对偶关系。
AI 中文摘要
Worley-Sagan插入和Haiman混合插入是用于移位Young表的插入算法，它们各自给出了n次对称群与由n个格子的同形状移位Young表对组成的集合之间的Robinson-Schensted型对应。已知这两种插入互为对偶。我们的目的是在不失去对偶关系的情况下推广这两种插入。推广后的插入算法将从着色排列生成移位表对。我们对Worley-Sagan插入的推广不同于Sagan本人“Knuth版本”对着色排列的限制。在证明我们推广的插入之间的对偶性时，我们通过“加倍”移位表将它们“嵌入”到Shimozono和White用于非移位表的双重混合插入中，并利用Shimozono和White所展示的双重混合插入的自对偶性。
英文摘要
The Worley-Sagan insertion and Haiman's mixed insertion are insertion algorithms for shifted Young tableaux, and each of them gives a Robinson-Schensted-type correspondence between the symmetric group of degree $n$ and a set consisting of certain pairs of same-shape shifted Young tableaux with $n$ cells. It is a known fact that these two insertions are dual to each other. Our purpose is to give an extension of these two insertions without losing the duality relationship. The extended ones will be insertions producing pairs of shifted tableaux from colored permutations. Our extension of the Worley-Sagan insertion is different from the restriction of Sagan's own "Knuth version" to colored permutations. In proving the duality between our extended insertions, we "embed" them into Shimozono and White's doubly mixed insertion for unshifted tableaux by "doubling" shifted tableaux and use the self-duality of the doubly mixed insertion shown by Shimozono and White.
Comments59 pages, 21 figures; corrected underlining in the PDF; mathematical content unchanged
