A note on the Formanek Weingarten function

Abstract

The aim of this note is to compare work of Formanek [7] on a certain construction of central polynomials with that of Collins [3] 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.