On polynomial integrals over the orthogonal group
Teodor Banica, Benoit Collins, Jean-Marc Schlenker

TL;DR
This paper studies integrals over the orthogonal group involving matrix entries, revealing invariance properties and providing a general factorial-based formula using combinatorial methods.
Contribution
It introduces new invariance properties and a comprehensive factorial formula for polynomial integrals over the orthogonal group, advancing theoretical understanding.
Findings
Identified invariance properties of polynomial integrals over O(n)
Derived a general factorial formula for these integrals
Used combinatorial methods to establish key results
Abstract
We consider integrals of type , with respect to the Haar measure on the orthogonal group. We establish several remarkable invariance properties satisfied by such integrals, by using combinatorial methods. We present as well a general formula for such integrals, as a sum of products of factorials.
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