On Square-Integrable Representations of A Lie Group of 4-Dimensional Standard Filiform Lie Algebra
In this paper, we study irreducible unitary representations of a real standard filiform Lie group with dimension equals 4 with respect to its basis. To find this representations we apply the orbit method introduced by Kirillov. The corresponding orbit of this representation is genereric orbits of di...
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| Format: | Article |
| Language: | English |
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Mathematics Department UIN Maulana Malik Ibrahim Malang
2020-05-01
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| Series: | Cauchy: Jurnal Matematika Murni dan Aplikasi |
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| Online Access: | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/9094 |
| _version_ | 1811337861021040640 |
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| author | Edi Kurniadi |
| author_facet | Edi Kurniadi |
| author_sort | Edi Kurniadi |
| collection | DOAJ |
| description | In this paper, we study irreducible unitary representations of a real standard filiform Lie group with dimension equals 4 with respect to its basis. To find this representations we apply the orbit method introduced by Kirillov. The corresponding orbit of this representation is genereric orbits of dimension 2. Furthermore, we show that obtained representation of this group is square-integrable. Moreover, in such case , we shall consider its Duflo-Moore operator as multiple of scalar identity operator. In our case that scalar is equal to one. |
| first_indexed | 2024-04-13T18:01:11Z |
| format | Article |
| id | doaj.art-ed11cc44c52c4773bc8432ff15a5c85e |
| institution | Directory Open Access Journal |
| issn | 2086-0382 2477-3344 |
| language | English |
| last_indexed | 2024-04-13T18:01:11Z |
| publishDate | 2020-05-01 |
| publisher | Mathematics Department UIN Maulana Malik Ibrahim Malang |
| record_format | Article |
| series | Cauchy: Jurnal Matematika Murni dan Aplikasi |
| spelling | doaj.art-ed11cc44c52c4773bc8432ff15a5c85e2022-12-22T02:36:14ZengMathematics Department UIN Maulana Malik Ibrahim MalangCauchy: Jurnal Matematika Murni dan Aplikasi2086-03822477-33442020-05-0162849010.18860/ca.v6i2.90945021On Square-Integrable Representations of A Lie Group of 4-Dimensional Standard Filiform Lie AlgebraEdi Kurniadi0Departemen Matematika FMIPA UnpadIn this paper, we study irreducible unitary representations of a real standard filiform Lie group with dimension equals 4 with respect to its basis. To find this representations we apply the orbit method introduced by Kirillov. The corresponding orbit of this representation is genereric orbits of dimension 2. Furthermore, we show that obtained representation of this group is square-integrable. Moreover, in such case , we shall consider its Duflo-Moore operator as multiple of scalar identity operator. In our case that scalar is equal to one.https://ejournal.uin-malang.ac.id/index.php/Math/article/view/9094duflo-moore operator, irreducible unitary representation, square-integrable representation, standard filiform lie algebra. |
| spellingShingle | Edi Kurniadi On Square-Integrable Representations of A Lie Group of 4-Dimensional Standard Filiform Lie Algebra Cauchy: Jurnal Matematika Murni dan Aplikasi duflo-moore operator, irreducible unitary representation, square-integrable representation, standard filiform lie algebra. |
| title | On Square-Integrable Representations of A Lie Group of 4-Dimensional Standard Filiform Lie Algebra |
| title_full | On Square-Integrable Representations of A Lie Group of 4-Dimensional Standard Filiform Lie Algebra |
| title_fullStr | On Square-Integrable Representations of A Lie Group of 4-Dimensional Standard Filiform Lie Algebra |
| title_full_unstemmed | On Square-Integrable Representations of A Lie Group of 4-Dimensional Standard Filiform Lie Algebra |
| title_short | On Square-Integrable Representations of A Lie Group of 4-Dimensional Standard Filiform Lie Algebra |
| title_sort | on square integrable representations of a lie group of 4 dimensional standard filiform lie algebra |
| topic | duflo-moore operator, irreducible unitary representation, square-integrable representation, standard filiform lie algebra. |
| url | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/9094 |
| work_keys_str_mv | AT edikurniadi onsquareintegrablerepresentationsofaliegroupof4dimensionalstandardfiliformliealgebra |