For each partition p– of an integer N≥2, consisting of r parts, an integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently by some of us. In the present paper we show that any tau-function of the p–-reduced r-component KP hierarchy produces a solution of this integrable hierarchy. Along the way we provide an algorithm for the explicit construction of the generators of the corresponding classical W-algebra W(glN,p–), and write down explicit formulas for evolution of these generators along the commuting Hamiltonian flows.

中文翻译：

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$$\underline{p}$$-reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$-algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$

对于由 r 个部分组成的整数 N≥2 的每个分区 p–，我们中的一些人最近构建了 Lax 型哈密顿偏微分方程的可积层次结构。在本文中，我们展示了 p– 约简 r 分量 KP 层次结构的任何 tau 函数都会产生该可积层次结构的解。在此过程中，我们提供了用于显式构造相应经典 W 代数 W(glN,p–) 的生成器的算法，并写下这些生成器沿交换哈密顿流演化的显式公式。