ABSTRACT
This chapter considers in detail the representations generated by the spin functions and by the spatial functions. It explores some of the basic notions of the irreducible representations of the symmetric group. The vector space is invariant with respect to the elements of the symmetric group if the application of an element on a vector leads to a new vector which is in the same space that is the result is a linear combination of the basis vectors. For the symmetric group each class is characterized by a partition of N, so the number of irreducible representations of SN is equal to the number of partitions of N. The chapter presents Young's theory of the representations of the symmetric group. Young worked out different representations of the symmetric group using the standard tableaux. The representation conjugate to the identity representation is called the alternating representation.
