Symmetric functions, codes of partitions and the KP hierarchy
Combinatorics
2009-02-26 v1 Algebraic Geometry
Abstract
We consider an operator of Bernstein for symmetric functions, and give an explicit formula for its action on an arbitrary Schur function. This formula is given in a remarkably simple form when written in terms of some notation based on the code of a partition. As an application, we give a new and very simple proof of a classical result for the KP hierarchy, which involves the Plucker relations for Schur function coefficients in a tau function for the hierarchy. This proof is especially compact because of a restatement that we give for the Plucker relations that is symmetrical in terms of partition code notation.
Keywords
Cite
@article{arxiv.0902.4441,
title = {Symmetric functions, codes of partitions and the KP hierarchy},
author = {S. R. Carrell and I. P. Goulden},
journal= {arXiv preprint arXiv:0902.4441},
year = {2009}
}