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

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

1994-11-07

arxiv.org/abs/hep-th/9411046v1

Mod.Phys.Lett. A10 (1995) 133-148

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, LaTex

Scientific paper

10.1142/S0217732395000156

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 ${\cal W}$ algebras on R.S. associated to each reduction are pointed out. The higher genus NLS hierarchy is analyzed in detail.

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