McKay Centralizer Algebras
For a finite subgroup G of the special unitary group SU2, we study the centralizer algebra Zk(G) = EndG(V⊗k) of G acting on the k-fold tensor product of its defining representation V = C2. The McKay corre- spondence relates the representation theory of these groups to an associated affine Dynkin dia...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/6360/pdf |
| _version_ | 1797270215677968384 |
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| author | Georgia Benkart Tom Halverson |
| author_facet | Georgia Benkart Tom Halverson |
| author_sort | Georgia Benkart |
| collection | DOAJ |
| description | For a finite subgroup G of the special unitary group SU2, we study the centralizer algebra Zk(G) = EndG(V⊗k) of G acting on the k-fold tensor product of its defining representation V = C2. The McKay corre- spondence relates the representation theory of these groups to an associated affine Dynkin diagram, and we use this connection to study the structure and representation theory of Zk(G) via the combinatorics of the Dynkin diagram. When G equals the binary tetrahedral, octahedral, or icosahedral group, we exhibit remarkable connections between Zk (G) and the Martin-Jones set partition algebras. |
| first_indexed | 2024-04-25T02:00:44Z |
| format | Article |
| id | doaj.art-8d3b3a9895214094bcd4db556d1fb255 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:44Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-8d3b3a9895214094bcd4db556d1fb2552024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.63606360McKay Centralizer AlgebrasGeorgia Benkart0Tom Halverson1Department of Mathematics [Madison]Department of Mathematics, Statistics, and Computer Science [Saint-Paul]For a finite subgroup G of the special unitary group SU2, we study the centralizer algebra Zk(G) = EndG(V⊗k) of G acting on the k-fold tensor product of its defining representation V = C2. The McKay corre- spondence relates the representation theory of these groups to an associated affine Dynkin diagram, and we use this connection to study the structure and representation theory of Zk(G) via the combinatorics of the Dynkin diagram. When G equals the binary tetrahedral, octahedral, or icosahedral group, we exhibit remarkable connections between Zk (G) and the Martin-Jones set partition algebras.https://dmtcs.episciences.org/6360/pdf[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Georgia Benkart Tom Halverson McKay Centralizer Algebras Discrete Mathematics & Theoretical Computer Science [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | McKay Centralizer Algebras |
| title_full | McKay Centralizer Algebras |
| title_fullStr | McKay Centralizer Algebras |
| title_full_unstemmed | McKay Centralizer Algebras |
| title_short | McKay Centralizer Algebras |
| title_sort | mckay centralizer algebras |
| topic | [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6360/pdf |
| work_keys_str_mv | AT georgiabenkart mckaycentralizeralgebras AT tomhalverson mckaycentralizeralgebras |