科研之友
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摘要
It is known that a class of special solutions of the Garnier system is expressed by a determinant formula in terms of a certain specialization of the Schur functions with rectangular-shape partitions. Y Yamada showed that such a determinant formula for rational solutions of Riccati type can be derived by making use of the Pade approximation. In this paper, we extend Yamada%26apos;s method. We derive a determinant formula for transcendental solutions of Riccati type by showing that the Pade approximation can be utilized in order to construct a Schlesinger transformation between isomonodromic deformations. In addition, we show that this method is effective in generic solutions of the Garnier system and derive a determinant structure of them.
- 出版日期2012-4-6
