Symmetric functions, codes of partitions and the KP hierarchy [article]

S.R. Carrell, I.P. Goulden
2009 arXiv   pre-print
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
more » ... ecause of a restatement that we give for the Plucker relations that is symmetrical in terms of partition code notation.
arXiv:0902.4441v1 fatcat:gbcjioadrvam3ctorcd6heknvi