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Representations of the Infinite-Dimensional Affine Group


Abstract

We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However it is possible to define its action on some classes of functions.

Вводиться нескінченновимірна аффінна група і будується її незвідне унітарне представлення. Наш підхід наслідує метод Вершика-Гельфанда-Граєва для групи дифеоморфізмів, з необхідними модифікаціями, пов’язаними з тим, що група не діє на фазовому просторі, але можна визначити її дію на деяких класах функцій.

Key words: Affine group; configurations; Poisson measure; ergodicity.


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Article Information

TitleRepresentations of the Infinite-Dimensional Affine Group
SourceMethods Funct. Anal. Topology, Vol. 26 (2020), no. 4, 348-355
DOI10.31392/MFAT-npu26_4.2020.06
MilestonesReeived 26/08/2020
CopyrightThe Author(s) 2020 (CC BY-SA)

Authors Information

Yuri Kondratiev
Department of Mathematis, University of Bielefeld, D-33615 Bielefeld, Germany; Dragomanov University, Kyiv, Ukraine


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Citation Example

Yuri Kondratiev, Representations of the Infinite-Dimensional Affine Group, Methods Funct. Anal. Topology 26 (2020), no. 4, 348-355.


BibTex

@article {MFAT1450,
    AUTHOR = {Yuri Kondratiev},
     TITLE = {Representations of the Infinite-Dimensional Affine Group},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {26},
      YEAR = {2020},
    NUMBER = {4},
     PAGES = {348-355},
      ISSN = {1029-3531},
       DOI = {10.31392/MFAT-npu26_4.2020.06},
       URL = {http://mfat.imath.kiev.ua/article/?id=1450},
}


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