Specht Modules and Representations of Symmetric Group

The symmetric group plays a key role in many areas of research in addition to mathematics and hence is of great importance. It is well known that representations of a symmetric group can be approached from three different directions: by using results from the general theory of group representations, by employing combinatorial techniques, or via symmetric functions. In this paper, we study the irreducible representations of symmetric groups by using the Specht Modules, which are irreducible sub-modules of the permutation modules. We provide a complete description of the construction of the irreducible representations via Young Symmetrizers (also called row and column stabilizers) and the Frobenius Formula. We explore a connection between Young Tableaux and the representation of the symmetric group \(S_n\) . We describe the construction of Specht Modules \(S^\lambda \) for each partition \(\lambda \) of n.