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