Symmetric Functions, Codes of Partitions and the Kp Hierarchy
نویسنده
چکیده
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 Plücker relations for Schur function coefficients in a τ -function for the hierarchy. This proof is especially compact because of a restatement that we give for the Plücker relations that is symmetrical in terms of partition code notation.
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