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An Elliptic Garnier System

Ormerod, Chris M. and Rains, Eric M. (2017) An Elliptic Garnier System. Communications in Mathematical Physics, 355 (2). pp. 741-766. ISSN 0010-3616. doi:10.1007/s00220-017-2934-6.

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We present a linear system of difference equations whose entries are expressed in terms of theta functions. This linear system is singular at 4m + 12 points for m ≥ 1, which appear in pairs due to a symmetry condition. We parameterize this linear system in terms of a set of kernels at the singular points. We regard the system of discrete isomonodromic deformations as an elliptic analogue of the Garnier system. We identify the special case in which m = 1 with the elliptic Painlevé equation; hence, this work provides an explicit form and Lax pair for the elliptic Painlevé equation.

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Additional Information:© 2017 Springer-Verlag GmbH Germany. Received: 21 December 2016; Accepted: 31 March 2017; First Online: 24 July 2017. The work of EMR was partially supported by the National Science Foundation under the Grant DMS-1500806.
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Issue or Number:2
Record Number:CaltechAUTHORS:20170725-124624205
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Official Citation:Ormerod, C.M. & Rains, E.M. Commun. Math. Phys. (2017) 355: 741.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79339
Deposited By: Tony Diaz
Deposited On:25 Jul 2017 20:07
Last Modified:15 Nov 2021 17:47

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