超特征、非交换变量中的对称函数及相关Hopf代数
组合数学
2012-01-24 v2 表示论
摘要
我们识别了两个看似不同的结构：超特征（一种在有限域上系数取值的幂幺上三角矩阵群上进行傅里叶分析的有效方法）以及非交换变量中的对称函数环。两者均为Hopf代数，并且作为Hopf代数同构。这使得各自领域的发展可以相互转移。这一识别为新兴的组合Hopf代数领域提供了丰富的一类例子。
引用
@article{arxiv.1009.4134,
title = {Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras},
author = {Marcelo Aguiar and Carlos Andre and Carolina Benedetti and Nantel Bergeron and Zhi Chen and Persi Diaconis and Anders Hendrickson and Samuel Hsiao and I. Martin Isaacs and Andrea Jedwab and Kenneth Johnson and Gizem Karaali and Aaron Lauve and Tung Le and Stephen Lewis and Huilan Li and Kay Magaard and Eric Marberg and Jean-Christophe Novelli and Amy Pang and Franco Saliola and Lenny Tevlin and Jean-Yves Thibon and Nathaniel Thiem and Vidya Venkateswaran and C. Ryan Vinroot and Ning Yan and Mike Zabrocki},
journal= {arXiv preprint arXiv:1009.4134},
year = {2012}
}
备注
To Appear in Advances in Mathematics (2012), 23 pages