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A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions
Репозиторій DSpace/Manakin
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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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A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions
Інший ID:
2010 Mathematics Subject Classification: 17B37; 20G42; 81R50; 17B80
DOI: http://dx.doi.org/10.3842/SIGMA.2013.049
DOI: http://dx.doi.org/10.3842/SIGMA.2013.049
Посилання:
A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Function / A. Kuniba, M. Okado, Y. Yamada // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 27 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.
The authors thank Ivan C.H. Ip, Anatol N. Kirillov, Toshiki Nakashima and Masatoshi Noumi
for communications. They also thank one of the referees for drawing attention to the references [9, 26]. This work is supported by Grants-in-Aid for Scientific Research No. 23340007,
No. 24540203, No. 23654007 and No. 21340036 from JSPS.
Дата:
2013
Переглядів:
654
Завантажень:
235
Анотація:
For a finite-dimensional simple Lie algebra g, let U⁺q(g) be the positive part of the quantized universal enveloping algebra, and Aq(g) be the quantized algebra of functions. We show that the transition matrix of the PBW bases of U⁺q(g) coincides with the intertwiner between the irreducible Aq(g)-modules labeled by two different reduced expressions of the longest element of the Weyl group of g. This generalizes the earlier result by Sergeev on A₂ related to the tetrahedron equation and endows a new representation theoretical interpretation with the recent solution to the 3D reflection equation for C₂. Our proof is based on a realization of U⁺q(g) in a quotient ring of Aq(g).
