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SIGMA, 2012, Volume 8, 036, 28 pages (Mi sigma713)  

This article is cited in 9 scientific papers (total in 9 papers)

CKP hierarchy, bosonic tau function and bosonization formulae

Johan W. van de Leura, Alexander Yu. Orlovb, Takahiro Shiotac

a Mathematical Institute, University of Utrecht, P.O. Box 80010, 3508 TA Utrecht, The Netherlands
b Nonlinear Wave Processes Laboratory, Oceanology Institute, 36 Nakhimovskii Prospect, Moscow 117851, Russia
c Mathematics Department, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan

Abstract: We develop the theory of CKP hierarchy introduced in the papers of Kyoto school [Date E., Jimbo M., Kashiwara M., Miwa T., J. Phys. Soc. Japan 50 (1981), 3806–3812] (see also [Kac V.G., van de Leur J.W., Adv. Ser. Math. Phys., Vol. 7, World Sci. Publ., Teaneck, NJ, 1989, 369–406]). We present appropriate bosonization formulae. We show that in the context of the CKP theory certain orthogonal polynomials appear. These polynomials are polynomial both in even and odd (in Grassmannian sense) variables.

Keywords: integrable system, Pfaffian, Hafnian, symmetric functions, Schur type functions

DOI: https://doi.org/10.3842/SIGMA.2012.036

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Bibliographic databases:

ArXiv: 1102.0087
Document Type: Article
MSC: 17B65; 17B67; 17B69; 20G43; 81R12
Received: January 17, 2012; in final form June 7, 2012; Published online June 22, 2012
Language: English

Citation: Johan W. van de Leur, Alexander Yu. Orlov, Takahiro Shiota, “CKP hierarchy, bosonic tau function and bosonization formulae”, SIGMA, 8 (2012), 036, 28 pp.

Citation in format AMSBIB
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\by Johan W. van de Leur, Alexander Yu. Orlov, Takahiro Shiota
\paper CKP hierarchy, bosonic tau function and bosonization formulae
\jour SIGMA
\yr 2012
\vol 8
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\totalpages 28
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Anguelova I.I., “Twisted Vertex Algebras, Bicharacter Construction and Boson-Fermion Correspondences”, J. Math. Phys., 54:12 (2013), 121702  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Chang L., Wu Ch.-Zh., “Tau Function of the Ckp Hierarchy and Nonlinearizable Virasoro Symmetries”, Nonlinearity, 26:9 (2013), 2577–2596  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Cheng J., He J., “The “Ghost” Symmetry in the Ckp Hierarchy”, J. Geom. Phys., 80 (2014), 49–57  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Anguelova I.I., Cox B., Jurisich E., “N-Point Locality for Vertex Operators: Normal Ordered Products, Operator Product Expansions, Twisted Vertex Algebras”, J. Pure Appl. Algebr., 218:12 (2014), 2165–2203  crossref  mathscinet  zmath  isi  elib  scopus
    5. Iana I. Anguelova, “Virasoro Structures in the Twisted Vertex Algebra of the Particle Correspondence of Type C”, Springer Proceedings in Mathematics and Statistics, 111 (2014), 435–446  crossref  mathscinet  zmath  scopus
    6. Anguelova I.I., “Multilocal Bosonization”, J. Math. Phys., 56:12 (2015), 121702  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. I. I. Anguelova, “The second bosonization of the CKP hierarchy”, J. Math. Phys., 58:7 (2017), 071707  crossref  mathscinet  zmath  isi  scopus
    8. B.-F. Feng, K.-I. Maruno, Ya. Ohta, “The Degasperis–Procesi equation, its short wave model and the CKP hierarchy”, Ann. Math. Sci. Appl., 2:2 (2017), 285–316  mathscinet  zmath  isi
    9. Li Ch., Li Sh.-H., “The Cauchy Two-Matrix Model, C-Toda Lattice and Ckp Hierarchy”, J. Nonlinear Sci., 29:1 (2019), 3–27  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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