Two-parameter quantum affine algebra \(U_{r,s}(\widehat{\mathfrak {sl}_n})\), Drinfel'd realization and quantum affine Lyndon basis
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Publication:930574
DOI10.1007/s00220-007-0405-1zbMath1236.17021arXiv0812.3107OpenAlexW3098429810MaRDI QIDQ930574
Marc Rosso, Honglian Zhang, Hu, Naihong
Publication date: 1 July 2008
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0812.3107
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50)
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Cites Work
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- Twisted vertex representations of quantum affine algebras
- On Drinfeld's realization of quantum affine algebras
- A two-parameter quantization of GL(n)
- The two-parameter quantum group of exceptional type \(G_2\) and Lusztig's symmetries
- The arithmetic theory of loop algebras
- Quantum groups and quantum shuffles
- A basis of type Poincaré-Birkhoff-Witt for the quantum algebra of \(\widehat{sl}(2)\)
- Braid group action and quantum affine algebras
- Convex bases of PBW type for quantum affine algebras
- Generalization of Drinfeld quantum affine algebras
- Drinfeld comultiplication and vertex operators
- The quantum Weyl group and the universal quantum \(R\)-matrix for affine Lie algebra \(A^{(1)}_ 1\)
- Two-parameter quantum groups and Drinfel'd doubles.
- On quantum shuffle and quantum affine algebras
- Drinfel'd doubles and Lusztig's symmetries of two-parameter quantum groups
- Vertex representations of quantum affine algebras
- Standard Lyndon Bases of Lie Algebras and Enveloping Algebras
- Quantum divided power algebra, \(q\)-derivatives, and some new quantum groups
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