English

A note on the Weingarten function

Mathematical Physics 2021-03-01 v6 math.MP

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.

Keywords

Cite

@article{arxiv.2008.11129,
  title  = {A note on the Weingarten function},
  author = {Claudio Procesi},
  journal= {arXiv preprint arXiv:2008.11129},
  year   = {2021}
}

Comments

this version corrects several mistakes and improves some of the presentation

R2 v1 2026-06-23T18:05:45.957Z