Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian
We introduce the class of controlled Loewner-Kufarev equations and consider aspects of their algebraic nature. We lift the solution of such a controlled equation to the (Sato)-Segal-Wilson Grassmannian, and discuss its relation with the tau-function. We briefly highlight relations of the Grunsky mat...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211012 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian. Takafumi Amaba and Roland Friedrich. SIGMA 16 (2020), 108, 25 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862646182513213440 |
|---|---|
| author | Amaba, Takafumi Friedrich, Roland |
| author_facet | Amaba, Takafumi Friedrich, Roland |
| citation_txt | Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian. Takafumi Amaba and Roland Friedrich. SIGMA 16 (2020), 108, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We introduce the class of controlled Loewner-Kufarev equations and consider aspects of their algebraic nature. We lift the solution of such a controlled equation to the (Sato)-Segal-Wilson Grassmannian, and discuss its relation with the tau-function. We briefly highlight relations of the Grunsky matrix with integrable systems and conformal field theory. Our main result is the explicit formula that expresses the solution of the controlled equation in terms of the signature of the driving function through the action of words in generators of the Witt algebra.
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| first_indexed | 2026-03-15T10:41:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211012 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T10:41:53Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Amaba, Takafumi Friedrich, Roland 2025-12-22T09:28:15Z 2020 Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian. Takafumi Amaba and Roland Friedrich. SIGMA 16 (2020), 108, 25 pages 1815-0659 2020 Mathematics Subject Classification: 35Q99; 30F10; 35C10; 58J65 arXiv:1809.00534 https://nasplib.isofts.kiev.ua/handle/123456789/211012 https://doi.org/10.3842/SIGMA.2020.108 We introduce the class of controlled Loewner-Kufarev equations and consider aspects of their algebraic nature. We lift the solution of such a controlled equation to the (Sato)-Segal-Wilson Grassmannian, and discuss its relation with the tau-function. We briefly highlight relations of the Grunsky matrix with integrable systems and conformal field theory. Our main result is the explicit formula that expresses the solution of the controlled equation in terms of the signature of the driving function through the action of words in generators of the Witt algebra. T.A. was supported by JSPS KAKENHI Grant Number 15K17562. R.F. was previously supported by the ERC advanced grant "Noncommutative distributions in free probability". Both authors thank Theo Sturm for the hospitality he offered to T.A. at the University of Bonn. T.A. thanks Roland Speicher for the hospitality offered himin Saarbrucken. R.F. thanks Roland Speicher for discussions, and Fukuoka University and the MPI in Bonn for their hospitality. We both thank Takuya Murayama for the discussions, comments, and collaboration. We thank the anonymous referees for their comments, which helped us to improve the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian Article published earlier |
| spellingShingle | Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian Amaba, Takafumi Friedrich, Roland |
| title | Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian |
| title_full | Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian |
| title_fullStr | Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian |
| title_full_unstemmed | Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian |
| title_short | Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian |
| title_sort | controlled loewner-kufarev equation embedded into the universal grassmannian |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211012 |
| work_keys_str_mv | AT amabatakafumi controlledloewnerkufarevequationembeddedintotheuniversalgrassmannian AT friedrichroland controlledloewnerkufarevequationembeddedintotheuniversalgrassmannian |