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arXiv · 0912.5273

On the Drinfeld-Sokolov Hierarchies of D type

Si-Qi Liu·Chao-Zhong Wu·Youjin Zhang
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Abstract

We extend the notion of pseudo-differential operators that are used to represent the Gelfand-Dickey hierarchies, and obtain a similar representation for the full Drinfeld-Sokolov hierarchies of $D_n$ type. By using such pseudo-differential operators we introduce the tau functions of these bi-Hamiltonian hierarchies, and prove that these hierarchies are equivalent to the integrable hierarchies defined by Date-Jimbo-Kashiware-Miwa and Kac-Wakimoto from the basic representation of the Kac-Moody algebra $D_n^{(1)}$.

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Si-Qi Liu, Chao-Zhong Wu, Youjin Zhang. 2009-12-30. On the Drinfeld-Sokolov Hierarchies of D type. https://arxiv.org/abs/0912.5273

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