# Regular, Quasi-regular and Induced Representations of Infinite-dimensional Groups

• ### Alexander V. Kosyak

National Academy of Science of Ukraine, Kiev, Ukraine

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 FrontmatterDownload pp. i–v PrefaceDownload pp. vii–xxv ContentsDownload pp. xxvii–xxxii 1 Introduction and Preliminariespp. 1–34 2 Regular representations of groups $B_0^\mathbb{N}$ and $B_0^\mathbb{Z}$pp. 35–109 3 Quasi-regular representations of the groups $B_0^\mathbb{N}$, $B_0^\mathbb{Z}$, and $G=$Bor$_0^\mathbb{N}$pp. 111–216 4 Quasi-regular representations of $B_0^\mathbb{N}$, product of m-dimensional Gaussian measurespp. 217–262 5 Elements of the modular theory for regular representationspp. 263–281 6 von Neumann algebras generated by the regular representationspp. 283–343 7 Induced representationspp. 345–384 8 Description of the dual for the groups $B_0^\mathbb{N}$ and $B_0^\mathbb{Z}$. First stepspp. 385–388 9 Ismagilov conjecture over a finite field $\mathbb{F}_p$pp. 389–478 10 Irreducibility of the Koopman representations of GL$_0(2\infty,\mathbb{R})$pp. 479–521 11 Regular representations of non-matrix infinite-dimensional groupspp. 523–531 12 How to construct a triple $(\overline{G},G,\mu)$ for an infinite-dimensional group $G$?pp. 533–538 Bibliographypp. 539–549 Indexpp. 551–555