KP hierarchies, polynomial and rational \({\mathcal W}\) algebras on Riemann surfaces: A global approach

DOI10.1142/S0217732395000156zbMATH Open1020.37580arXivhep-th/9411046MaRDI QIDQ2728152

Publication date: 31 July 2001

Published in: Modern Physics Letters A (Search for Journal in Brave)

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

c a l W

algebras on R.S. associated to each reduction are pointed out. The higher genus NLS hierarchy is analyzed in detail.

Full work available at URL: https://arxiv.org/abs/hep-th/9411046

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

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