On invariant measures for the group of diffeomorphisms of the circle

1996/12/29 by Doug Pickrell, Pickrell, Doug
Mathematics · #Advanced Algebra and Geometry #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.funct-an/9612009

Abstract

In a previous paper the author constructed biinvariant measures (possibly having values in a line bundle) for a loop group LK (with compact simply connected K) acting on the formal completion of its complexification LG. One motivation for this was to find a geometric construction for the unitary structure for the positive energy representations of LK. In this paper we pursue an analogous construction for the group of diffeomorphisms of the circle.

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