Quantum affine algebras and universal R-matrix with spectral parameter, II

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dc.creatorZhang, Yao-Zhong
dc.creatorGould, Mark D.
dc.date1993-07-02
dc.date1993-07-14
dc.date.accessioned2026-07-07T09:01:16Z
dc.date.available2026-07-07T09:01:16Z
dc.descriptionThis paper is an extended version of our previous short letter \cite{ZG2} and is attempted to give a detailed account for the results presented in that paper. Let $U_q({\cal G}^{(1)})$ be the quantized nontwisted affine Lie algebra and $U_q({\cal G})$ be the corresponding quantum simple Lie algebra. Using the previous obtained universal $R$-matrix for $U_q(A_1^{(1)})$ and $U_q(A_2^{(1)})$, we determine the explicitly spectral-dependent universal $R$-matrix for $U_q(A_1)$ and $U_q(A_2)$. We apply these spectral-dependent universal $R$-matrix to some concrete representations. We then reproduce the well-known results for the fundamental representations and we are also able to derive for the first time the extreamly explicit and compact formula of the spectral-dependent $R$-matrix for the adjoint representation of $U_q(A_2)$, the simplest nontrival case when the tensor product of the representations is {\em not} multiplicity-free.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/hep-th/9307008
dc.identifierhttp://arxiv.org/abs/hep-th/9307008
dc.identifierBull. Austral. Math. Soc. 51 (1995) 177
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/148264
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleQuantum affine algebras and universal R-matrix with spectral parameter, II
dc.typetext

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