论文标题
仿射对称组的符号插入和kazhdan-lusztig细胞
Sign insertion and Kazhdan-Lusztig cells of affine symmetric groups
论文作者
论文摘要
$ A $ A $的Kazhdan-Lusztig细胞的组合原理最初是由Lusztig，Shi和XI开发的。 Chmutov，Pylyavskyy和Yudovina在其工作的基础上引入了仿射基质 - 球构建（缩写AMBC），该结构类似于Robinson-Schensted的类似物。布拉西亚克（Blasiak）在他的分解代谢作品中开发了一种affine type $ a $的kazhdan-lusztig理论的另一种方法。他引入了符号插入算法，并猜想，如果一个人修复了双面单元，则符号插入过程的记录图表将独特地决定，并由左键独特地确定。在本文中，我们通过证明Blasiak的猜想来团结这两种方法。在此过程中，我们表明，我们引入的某些新操作称为部分旋转，将左单元格和右键的相交中的元素连接起来。最后，我们研究了Blasiak的符号插入和作用于Lascoux和Schützenberger定义的半标准年轻Tableaux集合的标准化图之间的联系。
Combinatorics of Kazhdan-Lusztig cells in affine type $A$ was originally developed by Lusztig, Shi, and Xi. Building on their work, Chmutov, Pylyavskyy, and Yudovina introduced the affine matrix-ball construction (abbreviated AMBC) which gives an analog of Robinson-Schensted correspondence for affine symmetric groups. An alternative approach to Kazhdan-Lusztig theory in affine type $A$ was developed by Blasiak in his work on catabolism. He introduced sign insertion algorithm and conjectured that if one fixes the two-sided cell, the recording tableau of sign insertion process determines uniquely and is determined uniquely by the left cell. In this paper we unite these two approaches by proving Blasiak's conjecture. In the process, we show that certain new operations we introduce called partial rotations connect the elements in the intersection of a left cell and a right cell. Lastly, we investigate the connection between Blasiak's sign insertion and the standardization map acting on the set of semi-standard Young tableaux defined by Lascoux and Schützenberger.
