Birkhoff decompositions and Iwasawa decompositions for loop groups

DOI10.2748/tmj/1113247803zbMath0996.22013OpenAlexW2025440365MaRDI QIDQ1598961

Vladimir Balan, Josef F. Dorfmeister

Publication date: 4 November 2002

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1113247803

zbMATH Keywords

loop groupsWiener algebrainfinite-dimensional Lie groupscompact Lie groupsmaximal torusBirkhoff and Iwasawa decompositionsreductive subgrouptangent group

Mathematics Subject Classification ID

Loop groups and related constructions, group-theoretic treatment (22E67) Semisimple Lie groups and their representations (22E46) Nilpotent and solvable Lie groups (22E25) General properties and structure of real Lie groups (22E15)

Related Items (8)

A loop group method for affine harmonic maps into Lie groups ⋮ Holomorphic representation of constant mean curvature surfaces in Minkowski space: consequences of non-compactness in loop group methods ⋮ Timelike minimal surfaces via loop groups ⋮ Generalized DPW method and an application to isometric immersions of space forms ⋮ Isomonodromy aspects of the \(tt^*\) equations of Cecotti and Vafa. III: Iwasawa factorization and asymptotics ⋮ Kostant, Steinberg, and the Stokes matrices of the tt*-Toda equations ⋮ Iwasawa decompositions of some infinite-dimensional Lie groups ⋮ Willmore surfaces in spheres: the DPW approach via the conformal Gauss map

Cites Work

• Infinite dimensional Lie algebras. An introduction
• Harmonic maps into Lie groups (classical solutions of the chiral model)
• Systems of PDEs obtained from factorization in loop groups
• Weierstrass type representation of harmonic maps into symmetric spaces
• Lie semigroups and their applications
• Weierstrass-type representation for harmonic maps into general symmetric spaces via loop groups
• Willmore immersions and loop groups
• On analytic fiber bundles. I: Holomorphic fiber bundles with infinite dimensional fibers
• Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle.
• Infinite flag varieties and conjugacy theorems
• Tangent Bundles of Homogeneous Spaces are Homogeneous Spaces
• A FACTORIZATION PROBLEM IN NORMED RINGS, FUNCTIONS OF ISOMETRIC AND SYMMETRIC OPERATORS AND SINGULAR INTEGRAL EQUATIONS
• Weierstraß-type representation of affine spheres
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