Pfaffian and determinantal tau functions

J.W. van de Leur; Alexander Orlov

doi:10.1007/s11005-015-0786-6

Pfaffian and determinantal tau functions

J.W. van de Leur, Alexander Orlov

Institute of Oceanology

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	1499-1531
Number of pages	33
Journal	Letters in Mathematical Physics
Volume	105
Issue number	11
DOIs	https://doi.org/10.1007/s11005-015-0786-6
Publication status	Published - Nov 2015

Keywords

integrable systems
Tau functions
BKP
DKP
two-component Toda lattice
Pfaff lattice
free fermions

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10.1007/s11005-015-0786-6

015-0786-6Final published version, 636 KBLicence: Taverne

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title = "Pfaffian and determinantal tau functions",

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",

author = "{van de Leur}, J.W. and Alexander Orlov",

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AU - van de Leur, J.W.

AU - Orlov, Alexander

PY - 2015/11

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N2 - 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.

AB - 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.

KW - integrable systems

KW - Tau functions

KW - BKP

KW - DKP

KW - two-component Toda lattice

KW - Pfaff lattice

KW - free fermions

U2 - 10.1007/s11005-015-0786-6

DO - 10.1007/s11005-015-0786-6

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VL - 105

SP - 1499

EP - 1531

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 11

ER -

Pfaffian and determinantal tau functions

Abstract

Keywords

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