Universal $R$-matrix of double parameter quantum affine algebra $U_{q,Q}({\hat {sl_2}})$

Fengchang Li; Masatake Maruyama; Hiroyuki Yamane

Universal $R$-matrix of double parameter quantum affine algebra $U_{q,Q}({\hat {sl_2}})$

Quantum Algebra 2026-03-31 v1 Representation Theory

Authors: Fengchang Li , Masatake Maruyama , Hiroyuki Yamane

Abstract

We give the explicit formula of the universal $R$ -matrix of a double parameter (or two-parameter, or multi-parameter) quantum affine algebra of type ${\mathrm{A}}_1^{(1)}$ . For $N$ with $q_{00}q_{01}$ being a primitive $N$ -th root of unity, we introduce its $2N$ -dimensional representation and explicitly calculate the $R$ -matrix associated with it via the universal $R$ -matrix.

Keywords

universal R-matrix quantum affine algebra double parameter $U_{q,Q}$ $\hat{sl_2}$

Cite

@article{arxiv.2603.27925,
  title  = {Universal $R$-matrix of double parameter quantum affine algebra $U_{q,Q}({\hat {sl_2}})$},
  author = {Fengchang Li and Masatake Maruyama and Hiroyuki Yamane},
  journal= {arXiv preprint arXiv:2603.27925},
  year   = {2026}
}

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32 pages, any comment is welcome

Universal $R$-matrix of double parameter quantum affine algebra $U_{q,Q}({\hat {sl_2}})$

Abstract

Keywords

Cite

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