Tres lecciones en combinatoria algebraica. II. Las funciones sim\'etricas y la teor\'{\i}a de representaciones

TL;DR

This paper explores the relationship between symmetric functions and the representation theory of the symmetric group within algebraic and geometric combinatorics, highlighting key results and open problems.

Contribution

It provides an exposition of the connection between symmetric functions and representation theory, advancing understanding in algebraic combinatorics.

Findings

Analysis of symmetric functions in representation theory

Identification of open problems in algebraic combinatorics

Connections established between combinatorial structures and group representations

Abstract

En esta serie de tres articulos, damos una exposicion de varios resultados y problemas abiertos en tres areas de la combinatoria algebraica y geometrica: las matrices totalmente no negativas, las representaciones del grupo simetrico, y los arreglos de hiperplanos. Esta segunda parte trata la coneccion entre las funciones simetricas y la teoria de representaciones. In this series of three articles, we give an exposition of various results and open problems in three areas of algebraic and geometric combinatorics: totally non-negative matrices, representations of the symmetric group, and hyperplane arrangements. This second part treats the connection between symmetric functions and representation theory.