English

On polynomial integrals over the orthogonal group

Mathematical Physics 2019-02-27 v2 math.MP

Abstract

We consider integrals of type Onu11a1...u1nanu21b1...u2nbndu\int_{O_n}u_{11}^{a_1}... u_{1n}^{a_n}u_{21}^{b_1}... u_{2n}^{b_n} 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.

Keywords

Cite

@article{arxiv.0910.1258,
  title  = {On polynomial integrals over the orthogonal group},
  author = {Teodor Banica and Benoit Collins and Jean-Marc Schlenker},
  journal= {arXiv preprint arXiv:0910.1258},
  year   = {2019}
}

Comments

20 pages

R2 v1 2026-06-21T13:55:16.386Z