Schur Polynomials and Crystal Graphs

Schur polynomials are fundamental objects in representation theory and combinatorics, and are connected to lots of different areas of math. Most simply, they are a set of symmetric polynomials that form the basis for the space of all symmetric polynomials. In the context of this paper, Schur polynomials arise in the representation theory of general linear groups by giving characters of representations, which is important because characters determine representations up to isomorphism. As fundamental as Schur polynomials are, they are still interesting to study. The goal of this project is to produce new formulas for Schur polynomials.