The orthogonal Weingarten formula in compact form

Details The orthogonal Weingarten formula in compact form The orthogonal Weingarten formula in compact form

2009-06-25

arxiv.org/abs/0906.4694v3

Lett. Math. Phys. 91 (2010), 105-118

Mathematics

Classical Analysis and ODEs

12 pages

Scientific paper

We present a compact formulation of the orthogonal Weingarten formula, with the traditional quantity $I(i_1,...,i_{2k}:j_1,...,j_{2k}) = \int_{O_n}u_{i_1j_1} ... u_{i_{2k}j_{2k}} du$ replaced by the more advanced quantity $I(a)=\int_{O_n}\Pi u_{ij}^{a_{ij}} du$, depending on a matrix of exponents $a\in M_n(\mathbb N)$. Among consequences, we establish a number of basic facts regarding the integrals $I(a)$: vanishing conditions, possible poles, asymptotic behavior.

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