Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method

Abstract

We extend the matrix-resolvent method for computing logarithmic derivatives of tau-functions to the Ablowitz--Ladik hierarchy. In particular, we derive a formula for the generating series of the logarithmic derivatives of an arbitrary tau-function in terms of matrix resolvents. As an application, we provide a way of computing certain integrals over the unitary group.

arXiv comment15 pages

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Cited by in corpus (2)

• Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, Circular $\beta$-ensemble and double confluent Heun equation
• Grothendieck's Dessins d'Enfants in a Web of Dualities. III