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Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups
Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data – S, T and fusion matrices – are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain identities on these tensor product or fusion multiplicities unde...
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Інститут математики НАН України
2013
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/149196 |
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irk-123456789-1491962019-02-20T01:25:53Z Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups Coquereaux, R. Zuber, J. Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data – S, T and fusion matrices – are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain identities on these tensor product or fusion multiplicities under conjugation of representations that had been discussed in our recent paper [J. Phys. A: Math. Theor. 44 (2011), 295208, 26 pages], proved to hold for simple and affine Lie algebras, and found to be generally wrong for finite groups. It is shown here that these identities fail also in general for Drinfeld doubles, indicating that modularity of the fusion category is not the decisive feature. Along the way, we collect many data on these Drinfeld doubles which are interesting for their own sake and maybe also in a relation with the theory of orbifolds in conformal field theory. 2013 Article Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups / R. Coquereaux, J. Zuber // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 53 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R50; 81T40; 20C99; 18D10 DOI: http://dx.doi.org/10.3842/SIGMA.2013.039 http://dspace.nbuv.gov.ua/handle/123456789/149196 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data – S, T and fusion matrices – are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain identities on these tensor product or fusion multiplicities under conjugation of representations that had been discussed in our recent paper [J. Phys. A: Math. Theor. 44 (2011), 295208, 26 pages], proved to hold for simple and affine Lie algebras, and found to be generally wrong for finite groups. It is shown here that these identities fail also in general for Drinfeld doubles, indicating that modularity of the fusion category is not the decisive feature. Along the way, we collect many data on these Drinfeld doubles which are interesting for their own sake and maybe also in a relation with the theory of orbifolds in conformal field theory. |
| format |
Article |
| author |
Coquereaux, R. Zuber, J. |
| spellingShingle |
Coquereaux, R. Zuber, J. Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Coquereaux, R. Zuber, J. |
| author_sort |
Coquereaux, R. |
| title |
Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups |
| title_short |
Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups |
| title_full |
Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups |
| title_fullStr |
Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups |
| title_full_unstemmed |
Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups |
| title_sort |
drinfeld doubles for finite subgroups of su(2) and su(3) lie groups |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149196 |
| citation_txt |
Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups / R. Coquereaux, J. Zuber // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 53 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT coquereauxr drinfelddoublesforfinitesubgroupsofsu2andsu3liegroups AT zuberj drinfelddoublesforfinitesubgroupsofsu2andsu3liegroups |
| first_indexed |
2023-05-20T17:32:12Z |
| last_indexed |
2023-05-20T17:32:12Z |
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1796153529403965440 |