Invariant Measures for Unitary Groups Associated to Kac-Moody Lie Algebras
Author: Doug Pickrell
Publisher: American Mathematical Soc.
Published: 2000
Total Pages: 143
ISBN-13: 0821820680
DOWNLOAD EBOOKThe main purpose of this paper is to prove the existence, and in some cases the uniqueness, of unitarily invariant measures on formal completions of groups associated to affine Kac-Moody algebras, and associated homogeneous spaces. The basic invariant measure is a natural generalization of Haar measure for a simply connected compact Lie group, and its projection to flag spaces is a generalization of the normalized invariant volume element. The other "invariant measures" are actually measures having values in line bundles over these spaces; these bundle-valued measures heuristically arise from coupling the basic invariant measure to Hermitian structures on associated line bundles, but in this infinite dimensional setting they are generally singular with respect to the basic invariant measure.