Tableaux, representaciones y la dualidad de Schur-Weyl

Abstract

The main objective of this work is to study the relation between representations of the symmetric group and those of the general linear group. This relation is known as the Schur-Weyl duality. We introduce the basic concepts of representation theory in the first chapter. In the second, use tableaux to construct all the irreducible representations of the symmetric group, and provide explicit homomorfisms to decompose the regular representation. Finally, in the third chapter, we use these representations to obtain polynomial representations for the general linear group, establishing the Schur-Weyl duality.