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.
Full Text
Article Information
| Title | Representations of the Infinite-Dimensional Affine Group |
| Source | Methods Funct. Anal. Topology, Vol. 26 (2020), no. 4, 348-355 |
| DOI | 10.31392/MFAT-npu26_4.2020.06 |
| MathSciNet |
MR4202434 |
| Milestones | Reeived 26/08/2020 |
| Copyright | The Author(s) 2020 (CC BY-SA) |
Authors Information
Yuri Kondratiev
Department of Mathematis, University of Bielefeld, D-33615 Bielefeld, Germany; Dragomanov University, Kyiv, Ukraine
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},
MRNUMBER = {MR4202434},
DOI = {10.31392/MFAT-npu26_4.2020.06},
URL = {http://mfat.imath.kiev.ua/article/?id=1450},
}
