CKP Hierarchy, Bosonic Tau Function and Bosonization Formulae

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.

References in corpus (2)

• Pfaffian structures and certain solutions to BKP hierarchies I. Sums over partitions
• Fermionic construction of tau functions and random processes

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• The "ghost" symmetry in the CKP hierarchy
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• CKP hierarchy and free Bosons
• Constrained Toda hierarchy and turning points of the Ruijsenaars-Schneider model
• Kadomtsev-Petviashvili hierarchies of types B and C
• Twisted vertex algebras, bicharacter construction and boson-fermion correspondences
• The generalized Giambelli formula and polynomial KP and CKP tau-functions
• Lagrangian Grassmannians, CKP hierarchy and hyperdeterminantal relations
• The second bosonization of the CKP hierarchy
• Multilocal bosonization
• Supersymmetric polynomials and algebro-combinatorial duality
• Correlation functions of charged free boson and fermion systems
• Quantum $W_{1+\infty }$ subalgebras of BCD type and symmetric polynomials