A note on the Weingarten function

DOI10.1285/I15900932V41N1P69arXiv2008.11129MaRDI QIDQ6347722

Publication date: 25 August 2020

Abstract: 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.

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05)

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