Branching rules in the ring of superclass functions of unipotent upper-triangular matrices
It is becoming increasingly clear that the supercharacter theory of the finite group of unipotent upper-triangular matrices has a rich combinatorial structure built on set-partitions that is analogous to the partition combinatorics of the classical representation theory of the symmetric group. This...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2009-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2698/pdf |
| _version_ | 1797270392082006016 |
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| author | Nathaniel Thiem |
| author_facet | Nathaniel Thiem |
| author_sort | Nathaniel Thiem |
| collection | DOAJ |
| description | It is becoming increasingly clear that the supercharacter theory of the finite group of unipotent upper-triangular matrices has a rich combinatorial structure built on set-partitions that is analogous to the partition combinatorics of the classical representation theory of the symmetric group. This paper begins by exploring a connection to the ring of symmetric functions in non-commuting variables that mirrors the symmetric group's relationship with the ring of symmetric functions. It then also investigates some of the representation theoretic structure constants arising from the restriction, tensor products and superinduction of supercharacters. |
| first_indexed | 2024-04-25T02:03:32Z |
| format | Article |
| id | doaj.art-f9f294241fd84636b81cf83bc56ecd67 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:32Z |
| publishDate | 2009-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-f9f294241fd84636b81cf83bc56ecd672024-03-07T14:45:40ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502009-01-01DMTCS Proceedings vol. AK,...Proceedings10.46298/dmtcs.26982698Branching rules in the ring of superclass functions of unipotent upper-triangular matricesNathaniel Thiem0University of Colorado [Boulder]It is becoming increasingly clear that the supercharacter theory of the finite group of unipotent upper-triangular matrices has a rich combinatorial structure built on set-partitions that is analogous to the partition combinatorics of the classical representation theory of the symmetric group. This paper begins by exploring a connection to the ring of symmetric functions in non-commuting variables that mirrors the symmetric group's relationship with the ring of symmetric functions. It then also investigates some of the representation theoretic structure constants arising from the restriction, tensor products and superinduction of supercharacters.https://dmtcs.episciences.org/2698/pdfset partitionssupercharactersbranching rulessymmetric functions[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Nathaniel Thiem Branching rules in the ring of superclass functions of unipotent upper-triangular matrices Discrete Mathematics & Theoretical Computer Science set partitions supercharacters branching rules symmetric functions [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Branching rules in the ring of superclass functions of unipotent upper-triangular matrices |
| title_full | Branching rules in the ring of superclass functions of unipotent upper-triangular matrices |
| title_fullStr | Branching rules in the ring of superclass functions of unipotent upper-triangular matrices |
| title_full_unstemmed | Branching rules in the ring of superclass functions of unipotent upper-triangular matrices |
| title_short | Branching rules in the ring of superclass functions of unipotent upper-triangular matrices |
| title_sort | branching rules in the ring of superclass functions of unipotent upper triangular matrices |
| topic | set partitions supercharacters branching rules symmetric functions [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2698/pdf |
| work_keys_str_mv | AT nathanielthiem branchingrulesintheringofsuperclassfunctionsofunipotentuppertriangularmatrices |