Séminaire Lotharingien de Combinatoire, B39e (1997), 26pp.

Bernd Fiedler

An Algorithm for the Decomposition of Ideals of
the Group Ring of a Symmetric Group

Abstract. We present an algorithm, which produces a decomposition of left or right ideals of the group ring of a symmetric group into minimal left or right ideals and a corresponding set of primitive pairwise orthogonal idempotents by means of a computer. The algorithm can be used to determine generating idempotents of (left or right) ideals which are given as sums or intersections of (left or right) ideals. We discuss several subjects such as minimal sets of test permutations and the application of fast Fourier transforms which contribute to a good efficiency of the algorithm. Further we show possibilities of use of the algorithm in the computer algebra of tensor expressions.

Received: January 30, 1998; Accepted: March 26, 1998.

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