Various methods for calculating reducible and irreducible representations of the symmetric group

Group Representation Theory has many uses in Physics and Chemistry, representations of the symmetric group being the most widely used. This thesis introduces Group Representation Theory and discusses various ways to calculate representations. The group most focused upon is the symmetric group. The first way to calculate representations of the symmetric group is by Young's natural representation which utilizes the fact that there is a one-to-one correspondence between Specht modules and the irreducible Sn -modules. The second way is to decompose the group algebra C&sqbl0;Sn&sqbr0; and find the representations of it which are the same as the group representations. This method uses Young operators which are irreducible idempotents and generate certain invariant subalgebras. Another method involves inducing representation of Sn from the known representation of Sn-1 . Numerous computations and examples are provided.