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This article is cited in 21 scientific papers (total in 21 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.
Received: January 17, 2012; in final form June 7, 2012; Published online June 22, 2012
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.
Linking options:
https://www.mathnet.ru/eng/sigma713 https://www.mathnet.ru/eng/sigma/v8/p36
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