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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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