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A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions
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)-mo...
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Інститут математики НАН України
2013
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/149342 |
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irk-123456789-1493422019-02-22T01:24:08Z A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions Kuniba, A. Okado, M. Yamada, Y. 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). 2013 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| 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). |
| format |
Article |
| author |
Kuniba, A. Okado, M. Yamada, Y. |
| spellingShingle |
Kuniba, A. Okado, M. Yamada, Y. A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Kuniba, A. Okado, M. Yamada, Y. |
| author_sort |
Kuniba, A. |
| title |
A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions |
| title_short |
A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions |
| title_full |
A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions |
| title_fullStr |
A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions |
| title_full_unstemmed |
A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions |
| title_sort |
common structure in pbw bases of the nilpotent subalgebra of uq(g) and quantized algebra of functions |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149342 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:32:45Z |
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