Infinite-dimensional flag manifolds in integrable systems

DOI10.1007/BF00996107zbMath0838.22008OpenAlexW4245738434MaRDI QIDQ1903557

Aloysius G. Helminck, Gerardus F. Helminck

Publication date: 30 May 1996

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00996107

zbMATH Keywords

linear systemsintegrable systemsflag varietiesDarboux transformationsline bundlesMiura transformintegrable deformations

Mathematics Subject Classification ID

Cites Work

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• Tau functions for the Dirac operator in the Euclidean plane
• Representations of the symmetric group, the specialization order, systems and Grassmann manifolds
• Determinants of Cauchy-Riemann operators as \(\tau\)-functions
• An algebro-geometric interpretation of the Bäcklund-transformation for the Korteweg-de Vries equation
• Loop groups and equations of KdV type
• Quantum field theory, Grassmannians, and algebraic curves
• On fermionic gauge groups, current algebras and Kac-Moody algebras
• Geometric realization of conformal field theory on Riemann surfaces
• Modifying Lax equations and the second Hamiltonian structure
• Infinite dimensional Grassmannian structure of two-dimensional quantum gravity
• Limit matrices for the Toda flow and periodic flags for loop groups
• The structure of Hilbert flag varieties
• Tau functions for the Dirac operator on the Poincaré disk
• The geometry of differential difference equations
• Commuting flows and conservation laws for Lax equations
• Infinite flag varieties and conjugacy theorems

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