On the R-matrix realization of quantum loop algebras

Abstract

We consider $\mathrm{R}$-matrix realization of the quantum deformations of the loop algebras $\tilde{\mathfrak{g}}$ corresponding to non-exceptional affine Lie algebras of type $\hat{\mathfrak{g}}=A_{N-1}^{(1)}$, $B_n^{(1)}$, $C_n^{(1)}$, $D_n^{(1)}$, $A_{N-1}^{(2)}$. For each $U_q(\tilde{\mathfrak{g}})$ we investigate the commutation relations between Gauss coordinates of the fundamental $\mathbb{L}$-operators using embedding of the smaller algebra into bigger one. The new realization of these algebras in terms of the currents is given. The relations between all off-diagonal Gauss coordinates and certain projections from the ordered products of the currents are presented. These relations are important in applications to the quantum integrable models.

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Cited by in corpus (5)

• Recurrence relations for off-shell Bethe vectors in trigonometric integrable models
• On the second realization for the positive part of $U_q(\widehat{s{l}_2})$ of equitable type
• R-Matrix presentation of quantum affine algebra in type $A_{2n-1}^{(2)}$
• On the R-matrix realization of the quantum loop algebra. The case of $U_q(D_n^{(2)})$
• Freidel-Maillet type presentations of $U_q(s{l}_2)$