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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)
DOI: http://dx.doi.org/10.1090/memo/0693
MathSciNet review: 1686655
MSC (1991): Primary 22E65; Secondary 17B37, 22E67, 58B25, 58D05

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Table of Contents


Chapters

  • General introduction
  • I. General theory
  • 1. The formal completions of and
  • 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
  • 3. The case
  • 4. The cases , , and
  • III. Loop groups
  • 0. Introduction for Part III
  • 1. Extensions of loop groups
  • 2. Completions of loop groups
  • 3. Existence of the measures ,
  • 4. Existence of invariant measures
  • IV. Diffeomorphisms of
  • 0. Introduction for Part IV
  • 1. Completions and classical analysis
  • 2. The extension and determinant formulas
  • 3. The measures , ,
  • 4. On existence of invariant measures