Regular, quasi-regular and induced representations of infinite-dimensional groups / Alexander Kosyak.
- Format:
-
- Author/Creator:
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- Series:
-
- Language:
- English
- Subjects (All):
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- Physical Description:
- xxxii, 555 pages ; 25 cm.
- Other Title:
- Representations of infinite-dimensional groups
- Place of Publication:
- Zürich, Switzerland : European Mathematical Society, [2018]
- Summary:
- "Almost all harmonic analysis on locally compact groups is based on the existence (and uniqueness) of a Haar measure. Therefore, it is very natural to attempt a similar construction for non-locally compact groups. The essential idea is to replace the non-existing Haar measure on an infinite-dimensional group by a suitable quasi-invariant measure on an appropriate completion of the initial group or on the completion of a homogeneous space. The aim of the book is a systematic development, by example, of noncommutative harmonic analysis on infinite-dimensional (non-locally compact) matrix groups. We generalize the notion of regular, quasi-regular and induced representations for arbitrary infinite-dimensional groups. The central idea to verify the irreducibility is the Ismagilov conjecture. We also extend the Kirillov orbit method for the group of upper triangular matrices of infinite order. In order to make the content accessible to a wide audience of nonspecialists, the exposition is essentially self-contained and very few prerequisites are needed. The book is aimed at graduate and advanced undergraduate students, as well as mathematicians who wish an introduction to representations of infinite-dimensional groups"--Back cover.
- Contents:
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- Introduction and preliminaries
- Regular representations of B₀N and B₀Z
- Quasi-regular representations of B₀N, B₀Z, and G=Bor₀N
- Quasi-regular representations of B₀N, product of m-dimensional Gaussian measures
- Elements of the modular theory for regular representations
- von Neumann algebras generated by the regular representations
- Induced representations
- Description of the dual for the groups B₀N and B₀Z. First steps
- Ismagilov conjecture over a finite field Fp
- Irreducibility of the Koopman representations of GL₀(2∞, R)
- Regular representations of non-matrix infinite-dimensional groups
- How to construct a triple (G̃, G, µ) for an infinite-dimensional group G?
- Notes:
- Includes bibliographical references (pages 539-549) and index.
- Other Format:
- Electronic version: Kosyak, Alexander V. Regular, quasi-regular and induced representations of infinite-dimensional groups.
- ISBN:
-
- OCLC:
- 1039615703
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