Pfaffian and determinantal tau functions
Publication date
2015-11
Authors
van de Leur, J.
Orlov, Alexander
Editors
Advisors
Supervisors
Document Type
Article
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taverne
Abstract
Adler, Shiota and van Moerbeke observed that a tau function of the Pfaff lattice is a square root of a tau function of the Toda lattice hierarchy of Ueno and Takasaki. In this paper, we give a representation theoretical explanation for this phenomenon. We consider 2-BKP and two-component 2-KP tau functions. We shall show that a square of a BKP tau function is equal to a certain two-component KP tau function and a square of a 2-BKP tau function is equal to a certain two-component 2-KP tau function.
Keywords
integrable systems, Tau functions, BKP, DKP, two-component Toda lattice, Pfaff lattice, free fermions, Taverne
Citation
van de Leur, J W & Orlov, A 2015, 'Pfaffian and determinantal tau functions', Letters in Mathematical Physics, vol. 105, no. 11, pp. 1499-1531. https://doi.org/10.1007/s11005-015-0786-6