Szegő Kernel and Symplectic Aspects of Spectral Transform for Extended Spaces of Rational Matrices
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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212027 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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-angle variables for the canonical symplectic form on the space of such functions. Comparison with previously known action-angle variables shows that the vector of Riemann constants is the gradient of some function on the moduli space of spectral curves; this function is found in the case of matrix dimension 2, when the spectral curve is hyperelliptic.
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| ISSN: | 1815-0659 |