On polynomial integrals over the orthogonal group
Abstract
We consider integrals of type ∫Onu11a1... u1nanu21b1... u2nbn du, 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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