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On polynomial integrals over the orthogonal group. (English) Zbl 1231.05282
Summary: We consider integrals of type \(\int_{O_n} u_{11}^{a_1} \cdots u_{1n}^{a_n}u^{b_1}_{21} \cdots u^{b_n}_{2n}du\), 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.

MSC:
05E10 Combinatorial aspects of representation theory
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