A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type
We present a representation of skew-orthogonal polynomials of symplectic type ( = 4) in terms of a matrix Riemann-Hilbert problem, for weights of the form e⁻ⱽ⁽ᶻ⁾ where is a polynomial of even degree and positive leading coefficient. This is done by representing skew-orthogonality as a kind of multi...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212344 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type. Alex Little. SIGMA 20 (2024), 076, 32 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862624453229281280 |
|---|---|
| author | Little, Alex |
| author_facet | Little, Alex |
| citation_txt | A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type. Alex Little. SIGMA 20 (2024), 076, 32 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present a representation of skew-orthogonal polynomials of symplectic type ( = 4) in terms of a matrix Riemann-Hilbert problem, for weights of the form e⁻ⱽ⁽ᶻ⁾ where is a polynomial of even degree and positive leading coefficient. This is done by representing skew-orthogonality as a kind of multiple-orthogonality. From this, we derive a = 4 analogue of the Christoffel-Darboux formula. Finally, our Riemann-Hilbert representation allows us to derive a Lax pair whose compatibility condition may be viewed as a = 4 analogue of the Toda lattice.
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| first_indexed | 2026-03-14T14:52:43Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212344 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T14:52:43Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Little, Alex 2026-02-05T09:54:17Z 2024 A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type. Alex Little. SIGMA 20 (2024), 076, 32 pages 1815-0659 2020 Mathematics Subject Classification: 60B20; 33C45; 30E15; 30E25 arXiv:2306.14107 https://nasplib.isofts.kiev.ua/handle/123456789/212344 https://doi.org/10.3842/SIGMA.2024.076 We present a representation of skew-orthogonal polynomials of symplectic type ( = 4) in terms of a matrix Riemann-Hilbert problem, for weights of the form e⁻ⱽ⁽ᶻ⁾ where is a polynomial of even degree and positive leading coefficient. This is done by representing skew-orthogonality as a kind of multiple-orthogonality. From this, we derive a = 4 analogue of the Christoffel-Darboux formula. Finally, our Riemann-Hilbert representation allows us to derive a Lax pair whose compatibility condition may be viewed as a = 4 analogue of the Toda lattice. The author would like to express his gratitude to Thomas Bothner and Mattia Cafasso, whose comments and suggestions have been invaluable for this paper. The author would also like to express his gratitude to the anonymous referees whose comments have improved the presentation of the paper and have drawn attention to connections to recent work. This work was supported by the UK Engineering and Physical Sciences Research Council through grant EP/T013893/2 and by the European Research Council (ERC) under the European Union Horizon 2020 research and innovation program (grant agreement No. 884584). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type Article published earlier |
| spellingShingle | A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type Little, Alex |
| title | A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type |
| title_full | A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type |
| title_fullStr | A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type |
| title_full_unstemmed | A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type |
| title_short | A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type |
| title_sort | riemann-hilbert approach to skew-orthogonal polynomials of symplectic type |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212344 |
| work_keys_str_mv | AT littlealex ariemannhilbertapproachtoskeworthogonalpolynomialsofsymplectictype AT littlealex riemannhilbertapproachtoskeworthogonalpolynomialsofsymplectictype |