A Lift of the Schur and Hall-Littlewood Bases to Non-commutative Symmetric Functions

Chris Berg; Nantel Bergeron; Franco Saliola; Luis Serrano; Mike Zabrocki

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A Lift of the Schur and Hall-Littlewood Bases to Non-commutative Symmetric Functions

机译：Schur和Hall-Littlewood基座对非交换对称函数的提升

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摘要

We introduce a new basis of the algebra of non-commutative symmetric functions whose images under the forgetful map are Schur functions when indexed by a partition. Dually, we build a basis of the quasi-symmetric functions that expand positively in the fundamental quasi-symmetric functions. We then use the basis to construct a non-commutative lift of the Hall-Littlewood symmetric functions with similar properties to their commutative counterparts.

机译：我们介绍了非交换对称函数代数的新基础，该对称函数的健忘映射下的图像在被分区索引时是Schur函数。双重地，我们建立了准对称函数的基础，该函数在基本准对称函数中正向扩展。然后，我们使用该基础构造Hall-Littlewood对称函数的非交换提升，其性质与它们的交换对应相似。

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来源
《Canadian Journal of Mathematics》 |2014年第3期|共41页
作者
Chris Berg; Nantel Bergeron; Franco Saliola; Luis Serrano; Mike Zabrocki;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Hall-Littlewood polynomial; symmetric function; quasisymmetric function; tableau.;

机译：Hall-Littlewood多项式对称函数拟对称函数平稳;

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专利

1. A Lift of the Schur and Hall-Littlewood Bases to Non-commutative Symmetric Functions [J] . Chris Berg, Nantel Bergeron, Franco Saliola, Canadian Journal of Mathematics . 2014,第3期

机译：Schur和Hall-Littlewood基座对非交换对称函数的提升
2. THE HOPF ALGEBRAS OF SYMMETRIC FUNCTIONS AND QUASI-SYMMETRIC FUNCTIONS IN NON-COMMUTATIVE VARIABLES ARE FREE AND CO-FREE [J] . Bergeron N, Zabrocki M Journal of algebra and its applications . 2009,第4期

机译：非交换变量的对称函数和拟对称函数的Hopf代数是免费的并且互为免费
3. Some new judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric functions [J] . Huan-Nan Shi, Jing Zhang Journal of inequalities and applications . 2013,第1期

机译：一类对称函数的Schur几何和Schur调和凸的一些新的判定定理
4. A Schur algorithm for symmetric inner functions [C] . Martine Olivi, Bernard Hanzon, Ralf L.M. Peeters, IEEE Conference on Decision and Control . 2005

机译：一种对称内函数的施核算法
5. The plethysm of two Schur functions at hook, near-hook, and two-row shapes and a class of (q,t)-symmetric functions arising for plethysm. [D] . Langley, Thomas. 2001

机译：钩形，近钩形和两行形的两个Schur函数的体积性和体积性产生的一类（q，t）对称函数。
6. Schur-convexity Schur-geometric and Schur-harmonic convexity for a composite function of complete symmetric function [O] . Huan-Nan Shi, Jing Zhang, Qing-Hua Ma -1

机译：完全对称函数的复合函数的Schur凸Schur几何和Schur调和凸
7. A lift of the Schur and Hall-Littlewood bases to non-commutative symmetric functions [O] . Berg, Chris, Bergeron, Nantel, Saliola, Franco, 2013

机译：舒尔和霍尔 - 利特伍德基地的电梯是非交换式的对称函数
8. Development of Three-Dimensional Pressure- Distribution Functions for Lifting Surfaces with Trailing-Edge Controls Based on the Integral Equation for Subsonic Flow [R] . Crespo, A. N., Cunningham, H. J. 1969

机译：基于亚音速流动积分方程的带有后缘控制的升力面三维压力分布函数的研制

A Lift of the Schur and Hall-Littlewood Bases to Non-commutative Symmetric Functions

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