Integration on loop groups. III: Asymptotic Peter-Weyl orthogonality

DOI10.1016/0022-1236(92)90145-9zbMath0762.22019OpenAlexW2080585052WikidataQ101069472 ScholiaQ101069472MaRDI QIDQ1196572

Marie-Paule Malliavin, Paul Malliavin

Publication date: 16 January 1993

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(92)90145-9

zbMATH Keywords

Wiener measureunitary representationsloop groupcurrent algebracentral extensionWiener convolution algebra

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Loop groups and related constructions, group-theoretic treatment (22E67) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Probability theory on linear topological spaces (60B11) Measures (Gaussian, cylindrical, etc.) on manifolds of maps (58D20)

Related Items (19)

COVER OF THE BROWNIAN BRIDGE AND STOCHASTIC SYMPLECTIC ACTION ⋮ De Rham-Hodge-Kodaira operator on loop groups ⋮ On \(Y M_ 2\) measures and area-preserving diffeomorphisms ⋮ Integration by parts for heat kernel measures revisited ⋮ Fokker-Planck equation with respect to heat measures on loop groups ⋮ An amenability-like property of finite energy path and loop groups ⋮ Heat Kernel Measures and Critical Limits ⋮ Integration on loop groups. II: Heat equation for the Wiener measure ⋮ Brownian pants and Deligne cohomology ⋮ A Cameron-Martin Type Quasi-Invariance Theorem for Pinned Brownian Motion on a Compact Riemannian Manifold ⋮ An invariant measure for the loop space of a simply connected compact symmetric space ⋮ Quasiregular representations of the infinite-dimensional nilpotent group ⋮ Integration by parts formula and logarithmic Sobolev inequality on the path space over loop groups ⋮ Differential calculus on path and loop spaces. II: Irreducibility of Dirichlet forms on loop spaces ⋮ Stochastic gauge transform of the string bundle ⋮ Representation of Green's function for the heat equation on a compact Lie group ⋮ Support of Virasoro unitarizing measures. ⋮ Hilbert Space of Spinor Fields Over the Free Loop Space ⋮ A unitary representation of the basical central extension of a loop group

Cites Work

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• Equations différentielles sur l'espace de Wiener et formules de Cameron- Martin non-linéaires
• Integration on loop groups. I: Quasi invariant measures
• Orbital theory for affine Lie algebras
• Measures on infinite dimensional Grassmann manifolds
• Temperature states on loop groups, theta functions and the Luttinger model
• Temperature states on loop groups, boson-fermion correspondence, and a determinant identity
• Integration on loop groups. II: Heat equation for the Wiener measure
• Théoremes de comparaison en géométrie Riemannienne

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