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

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CKP hierarchy, bosonic tau function and bosonization formulae

Johan W. van de Leur^a, Alexander Yu. Orlov^b, Takahiro Shiota^c

^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.

MSC: 17B65; 17B67; 17B69; 20G43; 81R12

Received: January 17, 2012; in final form June 7, 2012; Published online June 22, 2012

Language: English

DOI: 10.3842/SIGMA.2012.036