Irreducible Basis for Permutation Representations

W. Florek Computational Physics Division, Institute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

Received: July 13, 1999

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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.

DOI: 10.12693/APhysPolA.96.699 PACS numbers: 02.20.-a, 03.65.Bz