Noncommutative Analogs of Monomial Symmetric Functions, Cauchy Identity, and Hall Scalar Product
Combinatorics
2007-12-14 v1 Rings and Algebras
Abstract
This paper introduces noncommutative analogs of monomial symmetric functions and fundamental noncommutative symmetric functions. The expansion of ribbon Schur functions in both of these basis is nonnegative. With these functions at hand, one can derive a noncommutative Cauchy identity as well as study a noncommutative scalar product implied by Cauchy identity. This scalar product seems be the noncommutative analog of Hall scalar product in the commutative theory.
Keywords
Cite
@article{arxiv.0712.2201,
title = {Noncommutative Analogs of Monomial Symmetric Functions, Cauchy Identity, and Hall Scalar Product},
author = {Lenny Tevlin},
journal= {arXiv preprint arXiv:0712.2201},
year = {2007}
}
Comments
Based on the author's talk at FPSAC '07, Tianjin, China