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Representations of Infinite-Dimensional Groups
R. S. Ismagilov, Moscow Institute of Steel and Alloys, Russia

Translations of Mathematical Monographs
1996; 197 pp; hardcover
Volume: 152
ISBN-10: 0-8218-0418-9
ISBN-13: 978-0-8218-0418-6
List Price: US$96
Member Price: US$76.80
Order Code: MMONO/152
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This book is devoted to representations of two classes of infinite-dimensional groups: current groups and diffeomorphism groups. The author presents a complete treatment of the subject, including general methods for constructing irreducible representations of infinite-dimensional groups and general results about such representations. He also exhibits deep relations between representations of infinite-dimensional groups and the theory of Fock spaces, the theory of point random processes, and other branches of mathematics.


Graduate students and research mathematicians interested in representation theory, functional analysis, and mathematical physics.


"Very clear and will be useful to those who would become initiated in the theory of representations of current groups and diffeomorphism groups."

-- Mathematical Reviews

Table of Contents

  • Some general constructions related to representations
  • Representations of the group of measurable currents
  • Representations of the group of smooth currents
  • Certain results on diffeomorphism groups
  • Representations of diffeomorphism groups associated with configuration spaces
  • Representations of certain group extensions
  • Representations of diffeomorphism groups in the Fock space
  • Representations of groups of foliation preserving diffeomorphisms
  • References
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