arXiv subjects
Publications and source records attributed to Claire Gilson.
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.
This paper is devoted to revealing the relationship between matrix-valued $θ$-deformed bi-orthogonal polynomials and non-commutative Toda-type hierarchies. In this procedure, Wronski quasi-determinants are widely used and play the role of non-commutative $τ$-functions. At the same time, Bäcklund transformations are realized by using a moment modification method and non-commutative $θ$-deformed Volterra hierarchies are obtained, which contain the known examples of the Itoh-Narita-Bogoyavlensky lattices and the fractional Volterra hierarchy.