The aim of this note is to compare work of Formanek \cite{ formanek2} on a certain construction of central polynomials with that of Collins \cite{ 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 { \em Weingarten function}. By joining these two approaches we succeed in giving a simplified and { \em very natural} presentation of both Formanek and Collins's Theory.
Categories: math-ph math.MP
