A note on representations of the finite Heisenberg group and sums of greatest common divisors
We review an elementary approach to the construction of all irreducible representations of the finite Heisenberg group. Determining the number of inequivalent classes of irreducible representations by different methods leads to an identity of sums involving greatest common divisors. We show how this...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2001-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/284/pdf |
| _version_ | 1797270198523265024 |
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| author | Johannes Grassberger Günther Hörmann |
| author_facet | Johannes Grassberger Günther Hörmann |
| author_sort | Johannes Grassberger |
| collection | DOAJ |
| description | We review an elementary approach to the construction of all irreducible representations of the finite Heisenberg group. Determining the number of inequivalent classes of irreducible representations by different methods leads to an identity of sums involving greatest common divisors. We show how this identity can be generalized and derive an explicit formula for the sums. |
| first_indexed | 2024-04-25T02:00:27Z |
| format | Article |
| id | doaj.art-4e4d7e2d0adb46e7b338c38c56eb836d |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:27Z |
| publishDate | 2001-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-4e4d7e2d0adb46e7b338c38c56eb836d2024-03-07T15:04:11ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502001-01-01Vol. 4 no. 210.46298/dmtcs.284284A note on representations of the finite Heisenberg group and sums of greatest common divisorsJohannes Grassberger0Günther Hörmann1Abdus Salam International Centre for Theoretical Physics [Trieste]Fakultät für Mathematik [Wien]We review an elementary approach to the construction of all irreducible representations of the finite Heisenberg group. Determining the number of inequivalent classes of irreducible representations by different methods leads to an identity of sums involving greatest common divisors. We show how this identity can be generalized and derive an explicit formula for the sums.https://dmtcs.episciences.org/284/pdfheisenberg grouprepresentation of finite groupssums of gcds[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Johannes Grassberger Günther Hörmann A note on representations of the finite Heisenberg group and sums of greatest common divisors Discrete Mathematics & Theoretical Computer Science heisenberg group representation of finite groups sums of gcds [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | A note on representations of the finite Heisenberg group and sums of greatest common divisors |
| title_full | A note on representations of the finite Heisenberg group and sums of greatest common divisors |
| title_fullStr | A note on representations of the finite Heisenberg group and sums of greatest common divisors |
| title_full_unstemmed | A note on representations of the finite Heisenberg group and sums of greatest common divisors |
| title_short | A note on representations of the finite Heisenberg group and sums of greatest common divisors |
| title_sort | note on representations of the finite heisenberg group and sums of greatest common divisors |
| topic | heisenberg group representation of finite groups sums of gcds [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/284/pdf |
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