On q-symmetric functions and q-quasisymmetric functions

被引：4

作者：

Li, Yunnan ^{[1
,2
]}

机构：

[1] S China Univ Technol, Sch Sci, Guangzhou 510640, Guangdong, Peoples R China

[2] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2015年 / 41卷 / 02期

关键词：

q-Hopf algebra; Odd quasisymmetric Schur function; Littlewood-Richardson rule; HOPF ALGEBRA; DUALITY;

D O I：

10.1007/s10801-014-0538-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we construct the q-analogue of Poirier-Reutenauer algebras, related deeply with other q-combinatorial Hopf algebras. As an application, we use them to realize the odd Schur functions defined by Ellis, Khovanov, and Lauda, then naturally obtain the odd Littlewood-Richardson rule concerned by Ellis. Moreover, we construct the refinement of the odd Schur functions, called odd quasisymmetric Schur functions, parallel to the consideration by Haglund, Luoto, Mason, and van Willigenburg. All the q-Hopf algebras we discuss here provide the corresponding q-dual graded graphs.

引用

页码：323 / 364

页数：42