n-Schur Functions and Determinants on an Infinite Grassmannian
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- November 1998
- DOI:
- 10.48550/arXiv.math/9811081
- arXiv:
- arXiv:math/9811081
- Bibcode:
- 1998math.....11081K
- Keywords:
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- Algebraic Geometry;
- Mathematical Physics;
- Combinatorics