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Funktsional'nyi Analiz i ego Prilozheniya, 2019, Volume 53, Issue 4, Pages 63–78
DOI: https://doi.org/10.4213/faa3648 (Mi faa3648) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Spectral Curves of the Hyperelliptic Hitchin Systems

O. K. Sheinman

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (347 kB) Citations (7)
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DOI: https://doi.org/10.4213/faa3648
Abstract: This paper describes a class of spectral curves and gives explicit formulas for the Darboux coordinates of the Hitchin systems of types $A_l$, $B_l$, and $C_l$ on hyperelliptic curves. The current state of the problem in the case of the systems of type $D_l$ is described.
Received: 26.01.2019
Revised: 27.05.2019
Accepted: 08.08.2019
English version:
Functional Analysis and Its Applications, 2019, Volume 53, Issue 4, Pages 291–303
DOI: https://doi.org/10.1134/S0016266319040063
Bibliographic databases:
Document Type: Article
UDC: 514.8
Language: Russian
Citation: O. K. Sheinman, “Spectral Curves of the Hyperelliptic Hitchin Systems”, Funktsional. Anal. i Prilozhen., 53:4 (2019), 63–78; Funct. Anal. Appl., 53:4 (2019), 291–303
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/faa3648
  • https://doi.org/10.4213/faa3648
  • https://www.mathnet.ru/eng/faa/v53/i4/p63
    • This publication is cited in the following 7 articles:
    1. Russian Math. Surveys, 79:4 (2024), 683–720  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. O. K. Sheinman, “Separation of Variables for Hitchin Systems with the Structure Group $\mathrm {SO}(4)$ on Genus $2$ Curves”, Proc. Steklov Inst. Math., 325 (2024), 292–303  mathnet  crossref  crossref  zmath  isi
    3. P. Borisova, “Separation of variables for type $D_n$ Hitchin systems on a hyperelliptic curve”, Russian Math. Surveys, 76:2 (2021), 363–365  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. P. I. Borisova, O. K. Sheinman, “Hitchin Systems on Hyperelliptic Curves”, Proc. Steklov Inst. Math., 311 (2020), 22–35  mathnet  crossref  crossref  mathscinet  isi  elib
    5. O. K. Sheinman, “Quantization of integrable systems with spectral parameter on a Riemann surface”, Dokl. Math., 102:3 (2020), 524–527  mathnet  crossref  crossref  zmath  isi  elib
    6. O. K. Sheinman, “Spectral Curves of the Hyperelliptic Hitchin Systems”, Funct. Anal. Appl., 53:4 (2019), 291–303  mathnet  mathnet  crossref  crossref  mathscinet  isi  scopus
    7. O. K. Sheinman, “Integrable Systems of Algebraic Origin and Separation of Variables”, Funct. Anal. Appl., 52:4 (2018), 316–320  mathnet  mathnet  crossref  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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    References:60
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