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Jucys-Murphy elements and the unitary Weingarten function

Jonathan I. Novak — 2010

Banach Center Publications

We describe an approach to the unitary Weingarten function based on the JM elements of symmetric group algebras. When combined with previously known properties of the Weingarten function, this gives a surprising connection with the Moebius function of the lattice of noncrossing partitions.

Monotone Hurwitz Numbers and the HCIZ Integral

I. P. Goulden; Mathieu Guay-Paquet; Jonathan Novak — 2014

Annales mathématiques Blaise Pascal

In this article, we prove that the complex convergence of the HCIZ free energy is equivalent to the non-vanishing of the HCIZ integral in a neighbourhood of $z = 0$ . Our approach is based on a combinatorial model for the Maclaurin coefficients of the HCIZ integral together with classical complex-analytic techniques.

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