Extended T-System of Type G₂
We prove a family of 3-term relations in the Grothendieck ring of the category of finite-dimensional modules over the affine quantum algebra of type G₂ extending the celebrated T-system relations of type G₂. We show that these relations can be used to compute classes of certain irreducible modules,...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2013 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149348 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Extended T-System of Type G₂ / J. Li, E. Mukhin // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862637299676741632 |
|---|---|
| author | Li, J. Mukhin, E. |
| author_facet | Li, J. Mukhin, E. |
| citation_txt | Extended T-System of Type G₂ / J. Li, E. Mukhin // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove a family of 3-term relations in the Grothendieck ring of the category of finite-dimensional modules over the affine quantum algebra of type G₂ extending the celebrated T-system relations of type G₂. We show that these relations can be used to compute classes of certain irreducible modules, including classes of all minimal affinizations of type G₂. We use this result to obtain explicit formulas for dimensions of all participating modules.
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| first_indexed | 2025-11-30T22:44:20Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149348 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T22:44:20Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Li, J. Mukhin, E. 2019-02-21T07:06:53Z 2019-02-21T07:06:53Z 2013 Extended T-System of Type G₂ / J. Li, E. Mukhin // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B37; 81R50; 82B23 DOI: http://dx.doi.org/10.3842/SIGMA.2013.054 https://nasplib.isofts.kiev.ua/handle/123456789/149348 We prove a family of 3-term relations in the Grothendieck ring of the category of finite-dimensional modules over the affine quantum algebra of type G₂ extending the celebrated T-system relations of type G₂. We show that these relations can be used to compute classes of certain irreducible modules, including classes of all minimal affinizations of type G₂. We use this result to obtain explicit formulas for dimensions of all participating modules. This paper is a contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa. The full
 collection is available at http://www.emis.de/journals/SIGMA/InfiniteAnalysis2013.html.
 We would like to thank D. Hernandez, B. Leclerc, T. Nakanishi, C.A.S. Young for helpful
 discussions. JL would like to thank IUPUI Department of Mathematical Sciences for hospitality
 during his visit when this work was carried out. JL is partially supported by a CSC scholarship,
 the Natural Science Foundation of Gansu Province (No. 1107RJZA218), and the Fundamental
 Research Funds for the Central Universities (No. lzujbky-2012-12) from China. The research of
 EM is supported by the NSF, grant number DMS-0900984. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Extended T-System of Type G₂ Article published earlier |
| spellingShingle | Extended T-System of Type G₂ Li, J. Mukhin, E. |
| title | Extended T-System of Type G₂ |
| title_full | Extended T-System of Type G₂ |
| title_fullStr | Extended T-System of Type G₂ |
| title_full_unstemmed | Extended T-System of Type G₂ |
| title_short | Extended T-System of Type G₂ |
| title_sort | extended t-system of type g₂ |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149348 |
| work_keys_str_mv | AT lij extendedtsystemoftypeg2 AT mukhine extendedtsystemoftypeg2 |