KP Hierarchies, Polynomial and Rational W Algebras on Riemann Surfaces: a Global Approach

Abstract

A covariant pseudodifferential calculus on Riemann surfaces, based on the Krichever-Novikov global picture, is presented. It allows defining scalar and matrix KP operators, together with their reductions, in higher genus. Globally defined Miura maps are considered and the arising of polynomial or rational $\mathcal{W}$ algebras on R.S. associated to each reduction are pointed out. The higher genus NLS hierarchy is analyzed in detail.

arXiv comment15 pages, LaTex