Szegő Kernel and Symplectic Aspects of Spectral Transform for Extended Spaces of Rational Matrices

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• ISSN: 1815-0659
• Main Authors: Bertola, Marco, Korotkin, Dmitry, Sasani, Ramtin
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212027
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Szegő Kernel and Symplectic Aspects of Spectral Transform for Extended Spaces of Rational Matrices. Marco Bertola, Dmitry Korotkin and Ramtin Sasani. SIGMA 19 (2023), 104, 22 pages

We revisit the symplectic aspects of the spectral transform for matrix-valued rational functions with simple poles. We construct eigenvectors of such matrices in terms of the Szegő kernel on the spectral curve. Using variational formulas for the Szegő kernel, we construct a new system of action-angl...