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TMF, 2015, Volume 184, Number 2, Pages 212–243 (Mi tmf8875)  

This article is cited in 3 scientific papers (total in 3 papers)

Representations of $\mathfrak{sl}(2,\mathbb{C})$ in category $\mathcal O$ and master symmetries

J. P. Wang

School of Mathematics, Statistics and Actuarial Science, University of Kent, Kent, Canterbury, UK

Abstract: We show that the indecomposable $\mathfrak{sl}(2,\mathbb{C})$-modules in the Bernstein–Gelfand–Gelfand category $\mathcal O$ naturally arise for homogeneous integrable nonlinear evolution systems. We then develop a new approach called the $\mathcal O$ scheme to construct master symmetries for such integrable systems. This method naturally allows computing the hierarchy of time-dependent symmetries. We finally illustrate the method using both classical and new examples. We compare our approach to the known existing methods used to construct master symmetries. For new integrable equations such as a Benjamin–Ono-type equation, a new integrable Davey–Stewartson-type equation, and two different versions of $(2+1)$-dimensional generalized Volterra chains, we generate their conserved densities using their master symmetries.

Keywords: homogeneous integrable nonlinear equation, BGG category $\mathcal O$, master symmetry, conservation law, symmetry

Funding Agency Grant Number
Engineering and Physical Sciences Research Council EP/I038659/1


DOI: https://doi.org/10.4213/tmf8875

Full text: PDF file (705 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 184:2, 1078–1105

Bibliographic databases:

Document Type: Article
Received: 19.02.2015
Revised: 10.03.2015

Citation: J. P. Wang, “Representations of $\mathfrak{sl}(2,\mathbb{C})$ in category $\mathcal O$ and master symmetries”, TMF, 184:2 (2015), 212–243; Theoret. and Math. Phys., 184:2 (2015), 1078–1105

Citation in format AMSBIB
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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. A. V. Mikhailov, G. Papamikos, J. P. Wang, “Darboux transformation for the vector sine-Gordon equation and integrable equations on a sphere”, Lett. Math. Phys., 106:7 (2016), 973–996  crossref  mathscinet  zmath  isi  elib  scopus
    2. D. Talati, R. Turhan, “Two-component integrable generalizations of Burgers equations with nondiagonal linearity”, J. Math. Phys., 57:4 (2016), 041502  crossref  mathscinet  zmath  isi  elib  scopus
    3. R. Bury, A. V. Mikhailov, J. P. Wang, “Wave fronts and cascades of soliton interactions in the periodic two dimensional Volterra system”, Physica D, 347 (2017), 21–41  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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