论文标题
基于Domino Tableau类型的BSchur Potititive的观点
A domino tableau-based view on type B Schur-positivity
论文作者
论文摘要
在过去的几年中，人们对识别SCHUR阳性集的问题有了主要的关注，即，与之相关的准对称函数的排列集是对称的，并且可以写入非负相对称函数的总和。一组弧排列，即$ s_n $中的排列集$π$，使得任何$ 1 \ leq j \ leq n $，$ \ {π（1），π（2），\ dots，π（j）\} $是$ \ \ mathbb {z z} _n $的一个间隔。本文基于Chow的准对称函数和Domino Tableaux的生成功能，将SCHUR POTITITITION的新类型B扩展引入了签名的排列。作为一个重要的特征，我们的发展与所罗门关于Coxeter群体下降代数的作品兼容。特别是，我们设计了签名的电弧排列和多米诺骨牌tableaux集合之间的血液，以表明它们确实是B schur阳性的型。
Over the past years, major attention has been drawn to the question of identifying Schur-positive sets, i.e. sets of permutations whose associated quasisymmetric function is symmetric and can be written as a non-negative sum of Schur symmetric functions. The set of arc permutations, i.e. the set of permutations $π$ in $S_n$ such that for any $1\leq j \leq n$, $\{π(1),π(2),\dots,π(j)\}$ is an interval in $\mathbb{Z}_n$ is one of the most noticeable examples. This paper introduces a new type B extension of Schur-positivity to signed permutations based on Chow's quasisymmetric functions and generating functions for domino tableaux. As an important characteristic, our development is compatible with the works of Solomon regarding the descent algebra of Coxeter groups. In particular, we design descent preserving bijections between signed arc permutations and sets of domino tableaux to show that they are indeed type B Schur-positive.
