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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)
MathSciNet review: 1686655
MSC: Primary 22E65; Secondary 17B37, 22E67, 58B25, 58D05

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Table of Contents


  • 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
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