Discrete integrable systems and condensation algorithms for Pfaffians

Abstract

Inspired by the connection between the Dodgson's condensation algorithm and Hirota's difference equation, we consider condensation algorithms for Pfaffians from the perspectives of discrete integrable systems. The discretisation of Pfaffian elements demonstrate its effectiveness to the Pfaffian $\tau$-functions and discrete integrable systems. The free parameter in the discretisation allows us in particular to obtain explicit, one-parameter condensation algorithms for the Pfaffians.

14 pages; comments are welcome!

References in corpus (5)

• Condensation of Determinants
• The Cauchy two-matrix model
• Graphical Condensation Generalizations Involving Pfaffians and Determinants
• Hankel determinant solutions to several discrete integrable systems and the Laurent Property
• An inhomogeneous Lambda-determinant

Cited by in corpus (1)

• Christoffel transformations for (partial-)skew-orthogonal polynomials and applications