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Extended T-System of Type G₂
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Extended T-System of Type G₂
Інший ID:
2010 Mathematics Subject Classification: 17B37; 81R50; 82B23
DOI: http://dx.doi.org/10.3842/SIGMA.2013.054
DOI: http://dx.doi.org/10.3842/SIGMA.2013.054
Посилання:
Extended T-System of Type G₂ / J. Li, E. Mukhin // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 22 назв. — англ.
Підтримка:
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.
Дата:
2013
Переглядів:
510
Завантажень:
259
Анотація:
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.
