A note on the Weingarten function
Abstract
The aim of this note is to compare work of Formanek formanek2 on a certain construction of central polynomials with that of Collins Coll on integration on unitary groups. These two quite disjoint topics share the construction of the same function on the symmetric group, which the second author calls Weingarten function. By joining these two approaches we succeed in giving a simplified and very natural presentation of both Formanek and Collins's Theory.
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