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
$\tau$-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
$\tau$-functions as a sum with Plucker coordinates as coefficients.