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SIGMA, 2011, Volume 7, 049, 13 pp. (Mi sigma607)  

This article is cited in 1 scientific paper (total in 1 paper)

Symmetries in Connection Preserving Deformations

Christopher M. Ormerod

La Trobe University, Department of Mathematics and Statistics, Bundoora VIC 3086, Australia

Abstract: We wish to show that the root lattice of Bäcklund transformations of the $q$-analogue of the third and fourth Painlevé equations, which is of type $(A_2+A_1)^{(1)}$, may be expressed as a quotient of the lattice of connection preserving deformations. Furthermore, we will show various directions in the lattice of connection preserving deformations present equivalent evolution equations under suitable transformations. These transformations correspond to the Dynkin diagram automorphisms.

Keywords: $q$-Painlevé; Lax pairs; $q$-Schlesinger transformations; connection; isomonodromy

DOI: https://doi.org/10.3842/SIGMA.2011.049

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Full text: http://emis.mi.ras.ru/journals/SIGMA/2011/049/
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Bibliographic databases:

ArXiv: 1101.5422
MSC: 34M55; 39A13
Received: January 31, 2011; in final form May 18, 2011; Published online May 24, 2011
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Citation: Christopher M. Ormerod, “Symmetries in Connection Preserving Deformations”, SIGMA, 7 (2011), 049, 13 pp.

Citation in format AMSBIB
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\by Christopher M.~Ormerod
\paper Symmetries in Connection Preserving Deformations
\jour SIGMA
\yr 2011
\vol 7
\papernumber 049
\totalpages 13
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\crossref{https://doi.org/10.3842/SIGMA.2011.049}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855250867}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Christopher M. Ormerod, Eric M. Rains, “Commutation Relations and Discrete Garnier Systems”, SIGMA, 12 (2016), 110, 50 pp.  mathnet  crossref
  • Symmetry, Integrability and Geometry: Methods and Applications
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