Symmetric Functions in Noncommuting Variables
组合数学
2007-05-23 v2
摘要
Consider the algebra Q<<x_1,x_2,...>> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the variables and of bounded degree. We develop a theory of such functions analogous to the ordinary theory of symmetric functions. In particular, we define analogs of the monomial, power sum, elementary, complete homogeneous, and Schur symmetric functions as will as investigating their properties.
引用
@article{arxiv.math/0208168,
title = {Symmetric Functions in Noncommuting Variables},
author = {Mercedes H. Rosas and Bruce E. Sagan},
journal= {arXiv preprint arXiv:math/0208168},
year = {2007}
}
备注
16 pages, Latex, see related papers at http://www.math.msu.edu/~sagan, to appear in Transactions of the American Mathematical Society