# Invariant measures for unitary groups associated to Kac-Moody Lie algebras

### About this Title

**Doug Pickrell**

Publication: Memoirs of the American Mathematical Society

Publication Year
2000: Volume 146, Number 693

ISBNs: 978-0-8218-2068-1 (print); 978-1-4704-0284-6 (online)

DOI: http://dx.doi.org/10.1090/memo/0693

MathSciNet review: 1686655

MSC: Primary 22E65; Secondary 17B37, 22E67, 58B25, 58D05

### Table of Contents

**Chapters**

- General introduction
- I. General theory
- 1. The formal completions of $G(A)$ and $G(A)/B$
- 2. Measures on the formal flag space
- II. Infinite classical groups
- 0. Introduction for Part II
- 1. Measures on the formal flag space
- 2. The case $\mathfrak {g} = sl(\infty , \mathbb {C})$
- 3. The case $\mathfrak {g} = sl(2\infty , \mathbb {C})$
- 4. The cases $\mathfrak {g} = o(2\infty , \mathbb {C})$, $o(2\infty + 1, \mathbb {C})$, and $sp(\infty , \mathbb {C})$
- III. Loop groups
- 0. Introduction for Part III
- 1. Extensions of loop groups
- 2. Completions of loop groups
- 3. Existence of the measures $\nu _{\beta ,k}$, $\beta > 0$
- 4. Existence of invariant measures
- IV. Diffeomorphisms of $S^1$
- 0. Introduction for Part IV
- 1. Completions and classical analysis
- 2. The extension $\hat {\mathcal {D}}$ and determinant formulas
- 3. The measures $\nu _{\beta ,c,h}$, $\beta > 0$, $c,h \geq 0$
- 4. On existence of invariant measures