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Funktsional'nyi Analiz i ego Prilozheniya, 2003, Volume 37, Issue 1, Pages 78–81
DOI: https://doi.org/10.4213/faa138 (Mi faa138) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Brief communications

Irreducibility Criterion for Quasiregular Representations of the Group of Finite Upper Triangular Matrices

A. V. Kosyak

Institute of Mathematics, Ukrainian National Academy of Sciences
Full-text PDF (122 kB) Citations (6)
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DOI: https://doi.org/10.4213/faa138
Abstract: An analog of the quasiregular representation is defined for the group of infinite-order finite upper triangular matrices. It uses G-quasi-invariant measures on some G-spaces. The criterion for the irreducibility and equivalence of the constructed representations is given. This criterion allows us to generalize Ismagilov's conjecture on the irreducibility of an analog of regular representations of infinite-dimensional groups.
Keywords: Ismagilov's conjecture, quasiregular representation, infinite-dimensional group.
Received: 26.04.2002
English version:
Functional Analysis and Its Applications, 2003, Volume 37, Issue 1, Pages 65–68
DOI: https://doi.org/10.1023/A:1022928128185
Bibliographic databases:
Document Type: Article
UDC: 519.46
Language: Russian
Citation: A. V. Kosyak, “Irreducibility Criterion for Quasiregular Representations of the Group of Finite Upper Triangular Matrices”, Funktsional. Anal. i Prilozhen., 37:1 (2003), 78–81; Funct. Anal. Appl., 37:1 (2003), 65–68
Citation in format AMSBIB
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  • https://doi.org/10.4213/faa138
  • https://www.mathnet.ru/eng/faa/v37/i1/p78
    • This publication is cited in the following 6 articles:
    1. Kosyak A., “Criteria of Irreducibility of the Koopman Representations For the Group Gl(0)(2 Infinity, R)”, J. Funct. Anal., 276:1 (2019), 78–126  crossref  mathscinet  zmath  isi
    2. Kosyak A., “Regular, Quasi-Regular and Induced Representations of Infinite-Dimensional Groups”, Regular, Quasi-Regular and Induced Representations of Infinite-Dimensional Groups, Ems Tracts in Mathematics, 29, European Mathematical Soc, 2018, 1–555  mathscinet  zmath  isi
    3. Slowik R., “Real Elements in T-N(K)”, Linear Multilinear Algebra, 61:5 (2013), 667–677  crossref  mathscinet  zmath  isi  scopus
    4. Albeverio S., Kosyak A., “Quasiregular representations of the infinite-dimensional nilpotent group”, J. Funct. Anal., 236:2 (2006), 634–681  crossref  mathscinet  zmath  isi  scopus
    5. Albeverio S., Kosyak A., “Quasiregular representations of the infinite-dimensional Borel group”, J. Funct. Anal., 218:2 (2005), 445–474  crossref  mathscinet  zmath  isi  elib  scopus
    6. A. V. Kosyak, “Quasi-Invariant Measures and Irreducible Representations of the Inductive Limit of Special Linear Groups”, Funct. Anal. Appl., 38:1 (2004), 67–68  mathnet  mathnet  crossref  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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