Gelfand States and the Irreducible Representations of the Symmetric Group
- 1 April 1966
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 7 (4), 691-698
- https://doi.org/10.1063/1.1704983
Abstract
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.Keywords
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