Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2015
• 1. Verfasser: Kasman, A.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2015
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/147157
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity / A. Kasman // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 33 назв. — англ.

A wave function of the N-component KP Hierarchy with continuous flows determined by an invertible matrix H is constructed from the choice of an MN-dimensional space of finitely-supported vector distributions. This wave function is shown to be an eigenfunction for a ring of matrix differential operators in x having eigenvalues that are matrix functions of the spectral parameter z. If the space of distributions is invariant under left multiplication by H, then a matrix coefficient differential-translation operator in z is shown to share this eigenfunction and have an eigenvalue that is a matrix function of x. This paper not only generates new examples of bispectral operators, it also explores the consequences of non-commutativity for techniques and objects used in previous investigations.