Quasiregular representations of the infinite-dimensional Borel group

The notion of quasiregular (Representation of Lie groups, Nauka, Moscow, 1983) or geometric (Grundlehren der Mathematischen Wissenschaften, Band 220, Springer, Berlin, New York, 1976; Encyclopaedia of Mathematical Science, Vol. 22, Springer, Berlin, 1994, pp. 1–156) representation is well known for...

Full description

Saved in:
Bibliographic Details
Published in:Journal of functional analysis 2005-01, Vol.218 (2), p.445-474
Main Authors: Albeverio, Sergio, Kosyak, Alexandre
Format: Article
Language:English
Subjects:
Borel group
Ergodic measures
Infinite-dimensional groups
Irreducibility
Ismagilov conjecture
Quasi-invariant measures
Quasiregular (geometric) representations
Regular representations
Solvable group
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The notion of quasiregular (Representation of Lie groups, Nauka, Moscow, 1983) or geometric (Grundlehren der Mathematischen Wissenschaften, Band 220, Springer, Berlin, New York, 1976; Encyclopaedia of Mathematical Science, Vol. 22, Springer, Berlin, 1994, pp. 1–156) representation is well known for locally compact groups. In the present work an analog of the quasiregular representation for the solvable infinite-dimensional Borel group G=Bor 0 N is constructed and a criterion of irreducibility of the constructed representations is presented. This construction uses G-quasi-invariant Gaussian measures on some G-spaces X and extends the method used in Kosyak (Funktsional. Anal. i Priložhen 37 (2003) 78–81) for the construction of the quasiregular representations as applied to the nilpotent infinite-dimensional group B 0 N .
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2004.03.009