Quasi-Pfaffians and applications

2025/11/25 by Gilson, Claire, Li, Shi-Hao, Yu, Guo-Fu
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2511.19857

Abstract

This paper presents a non-commutative generalization of the Pfaffian which we call a quasi-Pfaffian. This novel concept arises from solving linear systems with non-commutative skew-symmetric coefficients. A new non-commutative integrable system whose solutions are expressed in terms of these quasi-Pfaffians is presented. Derivative formulae and identities satisfied by these quasi-Pfaffians are presented.

Citations

• Non-commutative multiple bi-orthogonal polynomials: formal approach and integrability
• Non-intersecting path explanation for block Pfaffians and applications into skew-orthogonal polynomials
• Multiple skew orthogonal polynomials and 2-component Pfaff lattice hierarchy
• Matrix-valued Cauchy bi-orthogonal polynomials and a novel noncommutative integrable lattice
• Matrix Orthogonal Polynomials, non-abelian Toda lattice and Bäcklund transformation
• Christoffel transformations for (partial-)skew-orthogonal polynomials and applications
• Discrete integrable systems and condensation algorithms for Pfaffians
• The Pfaff lattice on symplectic matrices
• On a direct approach to quasideterminant solutions of a noncommutative KP equation
• Nonabelian Integrable Systems, Quasideterminants, and Marchenko Lemma

Related

• Quasi-Pfaffian Solutions to Integrable Systems via Sylvester-Moutard Transformations
• Generalizations of the Pfaffian to non-antisymmetric matrices
• Formal Solutions of a Class of Pfaffian Systems in Two Variables
• A direct method in noncommutative integrable systems
• Formal Solutions of Completely Integrable Pfaffian Systems With Normal Crossings