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Journal of the London Mathematical Society Advance Access originally published online on October 17, 2007
Journal of the London Mathematical Society 2007 76(2):438-450; doi:10.1112/jlms/jdm064
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© 2007 London Mathematical Society

Middle convolution and deformation for Fuchsian systems

Yoshishige Haraoka

Department of Mathematics
School of Science
Kumamoto University
Kurokami
Kumamoto 860-8555
Japan

Galina Filipuk

Department of Mathematical Sciences
Loughborough University
Loughborough LE11 3TU
United Kingdom
g.filipuk{at}lboro.ac.uk

Middle convolution and addition are operations for Fuchsian systems of differential equations which preserve the number of accessory parameters. In this paper we show that they also preserve the deformation equations. Several Bäcklund transformations of the sixth Painlevé equation are obtained from this viewpoint.

2000 Mathematics Subject Classification 34M55.

Received May 31, 2006; published online October 17, 2007.


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