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Two-parameter Quantum Affine Algebra \(U_{r,s}(\widehat{\mathfrak {sl}_n})\), Drinfel’d Realization and Quantum Affine Lyndon Basis

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Abstract

We further define two-parameter quantum affine algebra \(U_{r,s}(\widehat{\mathfrak {sl}_n})\) (n > 2) after the work on the finite cases (see [BW1,BGH1,HS,BH]), which turns out to be a Drinfel’d double. Of importance for the quantum affine cases is that we can work out the compatible two-parameter version of the Drinfel’d realization as a quantum affinization of \(U_{r,s}({\mathfrak{sl}}_n)\) and establish the Drinfel’d Isomorphism Theorem in the two-parameter setting, via developing a new combinatorial approach (quantum calculation) to the quantum affine Lyndon basis we present (with an explicit valid algorithm based on the use of Drinfel’d generators).

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Min Hang Campus, Dong Chuan Road 500, Shanghai, 200241, PR China

    Naihong Hu & Honglian Zhang

  2. Départment Mathématiques et Applications, Ecole Normale Superieure, 45 Rue de Ulm, 75230, Paris Cedex 05, France

    Marc Rosso

  3. Department of Mathematics, Shanghai University, Shanghai, 200444, PR China

    Honglian Zhang

Authors
  1. Naihong Hu
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  2. Marc Rosso
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  3. Honglian Zhang
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Correspondence to Naihong Hu.

Additional information

Communicated by A. Connes

N.H., supported in part by the NNSF (Grants 10431040, 10728102), the PCSIRT, the TRAPOYT and the FUDP from the MOE of China, the SRSTP from the STCSM, die Deutche Forschungsgemeinschaft (DFG), as well as an ICTP long-term visiting scholarship.

H.Z., supported by a Ph.D. Program Scholarship Fund of ECNU 2006.

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Hu, N., Rosso, M. & Zhang, H. Two-parameter Quantum Affine Algebra \(U_{r,s}(\widehat{\mathfrak {sl}_n})\), Drinfel’d Realization and Quantum Affine Lyndon Basis. Commun. Math. Phys. 278, 453–486 (2008). https://doi.org/10.1007/s00220-007-0405-1

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  • DOI: https://doi.org/10.1007/s00220-007-0405-1

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