An Introduction to Schur Polynomials

TL;DR

This paper provides an introductory overview of Schur polynomials, covering their various expansions, combinatorial algorithms, and algebraic properties, based on lecture notes from a specialized workshop.

Contribution

It compiles and explains fundamental concepts and combinatorial tools related to Schur polynomials, serving as an educational resource for researchers and students.

Findings

Detailed explanation of Schur function expansions

Description of combinatorial algorithms like RSK and Schensted's insertion

Connections between Schur polynomials and Young tableaux

Abstract

Notes from a course at the ATM Workshop on Schubert Varieties, held at The Institute of Mathematical Sciences, Chennai, in November 2017. Various expansions of Schur functions, the Lindstr\"om-Gessel-Viennot lemma, semistandard Young tableaux, Schensted's insertion algorithm, the plactic monoid, the RSK correspondence, and the Littlewood-Richardson rule are discussed.