A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions
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| Creator |
Kuniba, A.
Okado, M. Yamada, Y. |
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| Description |
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).
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| Date |
2019-02-21T07:04:16Z
2019-02-21T07:04:16Z 2013 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 17B37; 20G42; 81R50; 17B80 DOI: http://dx.doi.org/10.3842/SIGMA.2013.049 http://dspace.nbuv.gov.ua/handle/123456789/149342 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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