Elementary Representations of the Group $B_0^ℤ$ of Upper-Triangular Matrices Infinite in Both Directions. I
We define so-called “elementary representations” $T_p^{R,µ},\; p ∈ ℤ$, of the group $B_0^ℤ$ of finite upper-triangular matrices infinite in both directions by using quasi-invariant measures on certain homogeneous spaces and give a criterion for the irreducibility and equivalence of the representatio...
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| Datum: | 2002 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4056 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510184989786112 |
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| author | Kosyak, O. V. Косяк, О. В. |
| author_facet | Kosyak, O. V. Косяк, О. В. |
| author_sort | Kosyak, O. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:20:24Z |
| description | We define so-called “elementary representations” $T_p^{R,µ},\; p ∈ ℤ$, of the group $B_0^ℤ$ of finite upper-triangular matrices infinite in both directions by using quasi-invariant measures on certain homogeneous spaces and give a criterion for the irreducibility and equivalence of the representations constructed. We also give a criterion for the irreducibility of the tensor product of finitely many and infinitely many elementary representations. |
| first_indexed | 2026-03-24T02:52:58Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4056 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:52:58Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/3b/f738d5f8ca33e9b28cf960e7631fe53b.pdf |
| spelling | umjimathkievua-article-40562020-03-18T20:20:24Z Elementary Representations of the Group $B_0^ℤ$ of Upper-Triangular Matrices Infinite in Both Directions. I Елементарні зображення групи $B_0^ℤ$ нескінченних в обидва боки верхнботрикутних матриць. І Kosyak, O. V. Косяк, О. В. We define so-called “elementary representations” $T_p^{R,µ},\; p ∈ ℤ$, of the group $B_0^ℤ$ of finite upper-triangular matrices infinite in both directions by using quasi-invariant measures on certain homogeneous spaces and give a criterion for the irreducibility and equivalence of the representations constructed. We also give a criterion for the irreducibility of the tensor product of finitely many and infinitely many elementary representations. Визначено так звані елементарні зображення $T_p^{R,µ},\; p ∈ ℤ$, групи $B_0^ℤ$ фінітних нескінченних на обидва боки верхньотрикутних матриць з використанням квазіінваріантних мір на деяких однорідних просторах і наведено критерій незвідності та еквівалентності побудованих зображень. Дано також критерій незвідності тензорного добутку скінченного та нескінченного числа елементарних зображень Institute of Mathematics, NAS of Ukraine 2002-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4056 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 2 (2002); 205-216 Український математичний журнал; Том 54 № 2 (2002); 205-216 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/4056/4822 https://umj.imath.kiev.ua/index.php/umj/article/view/4056/4823 Copyright (c) 2002 Kosyak O. V. |
| spellingShingle | Kosyak, O. V. Косяк, О. В. Elementary Representations of the Group $B_0^ℤ$ of Upper-Triangular Matrices Infinite in Both Directions. I |
| title | Elementary Representations of the Group $B_0^ℤ$ of Upper-Triangular Matrices Infinite in Both Directions. I |
| title_alt | Елементарні зображення групи $B_0^ℤ$
нескінченних в обидва боки
верхнботрикутних матриць. І |
| title_full | Elementary Representations of the Group $B_0^ℤ$ of Upper-Triangular Matrices Infinite in Both Directions. I |
| title_fullStr | Elementary Representations of the Group $B_0^ℤ$ of Upper-Triangular Matrices Infinite in Both Directions. I |
| title_full_unstemmed | Elementary Representations of the Group $B_0^ℤ$ of Upper-Triangular Matrices Infinite in Both Directions. I |
| title_short | Elementary Representations of the Group $B_0^ℤ$ of Upper-Triangular Matrices Infinite in Both Directions. I |
| title_sort | elementary representations of the group $b_0^ℤ$ of upper-triangular matrices infinite in both directions. i |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4056 |
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