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## Acta Physica Polonica A

1999 | 96 | 6 | 699-712
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### Irreducible Basis for Permutation Representations

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For a given finite group G its permutation representation P, i.e. an action on an n-element set, is considered. Introducing a vector space L as a set of formal linear combinations of | j 〉, 1 ≤ j ≤ n, the representation P is linearized. In general, the representation obtained is reducible, so it is decomposed into irreducible components. Decomposition of L into invariant subspaces is determined by a unitary transformation leading from the basis { | j 〉} to a new, symmetry adapted or irreducible, basis { |Γrγ〉}. This problem is quite generally solved by means of the so-called Sakata matrix. Some possible physical applications are indicated.
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699-712
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1999-12