Gelfand States and the Irreducible Representations of the Symmetric Group

The set of Gelfand states corresponding to a given partition [h1 … hn] form a basis for an irreducible representation of the unitary group Un. The special Gelfand states are defined as those for which [h1 … hn] is a partition of n and the weight is restricted to (11 … 1). We show that the special Gelfand states constitute basis for the irreducible representations of the symmetric group Sn and use this property to construct explicitly states in configuration and spin-isospin space with definite permutational symmetry.