On some properties of orthogonal Weingarten functions

Details On some properties of orthogonal Weingarten functions On some properties of orthogonal Weingarten functions

2009-03-30

arxiv.org/abs/0903.5143v1

Journal of Mathematical Physics 50 (2009), 113516

Physics

Mathematical Physics

18 pages, 0 figure

Scientific paper

We give a Fourier-type formula for computing the orthogonal Weingarten formula. The Weingarten calculus was introduced as a systematic method to compute integrals of polynomials with respect to Haar measure over classical groups. Although a Fourier-type formula was known in the unitary case, the orthogonal counterpart was not known. It relies on the Jack polynomial generalization of both Schur and zonal polynomials. This formula substantially reduces the complexity involved in the computation of Weingarten formulas. We also describe a few more new properties of the Weingarten formula, state a conjecture and give a table of values.

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