n-Schur Functions and Determinants on an Infinite Grassmannian

الأصل · EN

A set of functions is defined which is indexed by a positive integer n and partitions of integers. The case n=1 reproduces the standard Schur polynomials. These functions are seen to arise naturally as a determinant of an action on the frame bundle of an infinite grassmannian. This fact is well known in the case of the Schur polynomials (n=1) and has been used to decompose the τ-functions of the KP hierarchy as a sum. In the same way, the new functions introduced here (n>1) are used to expand quotients of τ-functions as a sum with Plucker coordinates as coefficients.