2012/03/31 by Chao-Zhong Wu
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.MP #math.RT
published as Adv. Math. 306 (2017), 603--652 · 45 pages. Some references are added and typos are corrected
arxiv created 2014/05/20 · arxiv updated 2017/08/29
For each Drinfeld-Sokolov integrable hierarchy associated to affine Kac-Moody algebra, we obtain a uniform construction of tau function by using tau-symmetric Hamiltonian densities, moreover, we represent its Virasoro symmetries as linear/nonlinear actions on the tau function. The relations between the tau function constructed in this paper and those defined for particular cases of Drinfeld-Sokolov hierarchies in the literature are clarified. We also show that, whenever the affine Kac-Moody algebra is simply-laced or twisted, the tau functions of the Drinfeld-Sokolov hierarchy coincide with the solutions of the corresponding Kac-Wakimoto hierarchy from the principal vertex operator realization of the affine algebra.