**Memoirs of the American Mathematical Society**

2000;
125 pp;
Softcover

MSC: Primary 58; 22;

Print ISBN: 978-0-8218-2068-1

Product Code: MEMO/146/693

List Price: $53.00

Individual Member Price: $31.80

**Electronic ISBN: 978-1-4704-0284-6
Product Code: MEMO/146/693.E**

List Price: $53.00

Individual Member Price: $31.80

# Invariant Measures for Unitary Groups Associated to Kac-Moody Lie Algebras

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*Doug Pickrell*

The 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.

#### Readership

Researchers in Lie groups, representation theory, stochastic analysis and geometry, and conformal field theory.