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 Dn type. By using such pseudo-differential operators, we introduce the tau functions of these bihamiltonian 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 Dn(1).

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