Supercharacters of Unipotent Groups
\textbfAbstract. We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters of algebra groups. The resulting superchar...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2014-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2383/pdf |
| _version_ | 1827323949913997312 |
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| author | Scott Andrews |
| author_facet | Scott Andrews |
| author_sort | Scott Andrews |
| collection | DOAJ |
| description | \textbfAbstract. We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters of algebra groups. The resulting supercharacter theories agree with those of André and Neto in the case of the unipotent orthogonal and symplectic matrices and generalize to a large collection of subgroups. In the unitary group case, we describe the supercharacters and superclasses in terms of labeled set partitions and calculate the supercharacter table. \bigbreak |
| first_indexed | 2024-04-25T02:02:02Z |
| format | Article |
| id | doaj.art-a66f560abdd6465caaa4be1450d6715b |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:02Z |
| publishDate | 2014-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-a66f560abdd6465caaa4be1450d6715b2024-03-07T14:53:19ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502014-01-01DMTCS Proceedings vol. AT,...Proceedings10.46298/dmtcs.23832383Supercharacters of Unipotent GroupsScott Andrews0University of Colorado [Boulder]\textbfAbstract. We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters of algebra groups. The resulting supercharacter theories agree with those of André and Neto in the case of the unipotent orthogonal and symplectic matrices and generalize to a large collection of subgroups. In the unitary group case, we describe the supercharacters and superclasses in terms of labeled set partitions and calculate the supercharacter table. \bigbreakhttps://dmtcs.episciences.org/2383/pdfsupercharacterrepresentation theoryunipotent grouplabeled set partition[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Scott Andrews Supercharacters of Unipotent Groups Discrete Mathematics & Theoretical Computer Science supercharacter representation theory unipotent group labeled set partition [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| title | Supercharacters of Unipotent Groups |
| title_full | Supercharacters of Unipotent Groups |
| title_fullStr | Supercharacters of Unipotent Groups |
| title_full_unstemmed | Supercharacters of Unipotent Groups |
| title_short | Supercharacters of Unipotent Groups |
| title_sort | supercharacters of unipotent groups |
| topic | supercharacter representation theory unipotent group labeled set partition [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/2383/pdf |
| work_keys_str_mv | AT scottandrews supercharactersofunipotentgroups |