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
Datum:2013
Hauptverfasser: Li, J., Mukhin, E.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2013
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
id nasplib_isofts_kiev_ua-123456789-149348
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Extended T-System of Type G₂
spellingShingle Extended T-System of Type G₂
Li, J.
Mukhin, E.
title_short 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_sort extended t-system of type g₂
author Li, J.
Mukhin, E.
author_facet Li, J.
Mukhin, E.
publishDate 2013
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/149348
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.
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AT mukhine extendedtsystemoftypeg2
first_indexed 2025-11-30T22:44:20Z
last_indexed 2025-11-30T22:44:20Z
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