CKP Hierarchy, Bosonic Tau Function and Bosonization Formulae

Symmetry Integrability and Geometry-Methods and Applications

article

Johan W. van de Leur¹  Alexander Yu. Orlov²  Takahiro Shiota³ 

[1] Mathematical Institute, University of Utrecht;Nonlinear Wave Processes Laboratory, Oceanology Institute;Mathematics Department, Faculty of Science, Kyoto University

关键词: integrable system;    Pfaffian;    Hafnian;    symmetric functions;    Schur type functions;   

DOI  :  10.3842/SIGMA.2012.036

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown