| Popis: |
This study centers on Schur polynomials, which are a linear basis of the ring of symmetric polynomials and have significant applications in representation theory. Our focus is on decreasing operators, which are well-defined for Schur polynomials and determine their product. We also present practical techniques for computing Littlewood-Richardson coefficients. By adopting this new perspective on Schur polynomials, we offer a novel proof of Pieri's rule that does not rely on geometry or forms for Schur functions. Our hope is that this new proof will shed light on subtraction free methods for calculating the product of two arbitrary Schur polynomials, as well as the product of a broader class of polynomials. |
