On polynomial integrals over the orthogonal group

We consider integrals of type On ua1 11 . . . uan 1nub1 21 . . . ubn 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.

• Type: Journal
• Year: 2011
• Where: JCT
• Authors: Teodor Banica, Benoit Collins, Jean-Marc Schlenker
• Keywords: Integrals, JCT 2011, Remarkable Invariance Properties, Ubn 2n Du