TL;DR
This paper offers a concise proof of a recent formula for the Weingarten matrix of the orthogonal group, utilizing Jucys-Murphy elements to simplify the derivation.
Contribution
It introduces a compact proof of the Collins-Matsumoto formula for orthogonal Weingarten matrices using Jucys-Murphy elements, streamlining previous derivations.
Findings
Simplified proof of the Weingarten matrix formula
Application of Jucys-Murphy elements in orthogonal group analysis
Enhanced understanding of orthogonal Weingarten matrices
Abstract
We provide a compact proof of the recent formula of Collins and Matsumoto for the Weingarten matrix of the orthogonal group using Jucys-Murphy elements.
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