A representation of a group is a group effect on a vector space; that is, for each element of the group we have an isomorphism of the vector space and its links are compatible with the multiplication of the group. In this seminar we will look at the representation theory of finite groups and especially symmetric groups. Several prominent mathematicians (such as Frobenius, Schur and Young) have studied the representation theory of symmetric groups. Furthermore, the representation theory of symmetric groups has connections with combinatorics and geometry, and has applications in mathematical physics and stochastics. Each representation is composed of irreducible representations and the main goal of the seminar is to describe these irreducible representations combinatorially with so-called Young diagrams.

G. D. James "The representation theory of the symmetric group" Springer, Lecture Notes in Mathemtaics vol 682, 1978

B. E. Sagan "The Symmetric Group - Representations, Combinatorial Algorithms, and Symmetric Functions" 2nd Edition, 2000