CaltechAUTHORS
  A Caltech Library Service

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. http://resolver.caltech.edu/CaltechAUTHORS:20170725-124624205

[img] PDF - Submitted Version
See Usage Policy.

308Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20170725-124624205

Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00220-017-2934-6DOIArticle
https://link.springer.com/article/10.1007%2Fs00220-017-2934-6PublisherArticle
https://arxiv.org/abs/1607.07831arXivDiscussion Paper
http://rdcu.be/utGjPublisherFree ReadCube access
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.
Funders:
Funding AgencyGrant Number
NSFDMS-1500806
Record Number:CaltechAUTHORS:20170725-124624205
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170725-124624205
Official Citation:Ormerod, C.M. & Rains, E.M. Commun. Math. Phys. (2017) 355: 741. https://doi.org/10.1007/s00220-017-2934-6
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79339
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 Jul 2017 20:07
Last Modified:25 Aug 2017 18:52

Repository Staff Only: item control page