TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.12.5.146
TI  - On the R-matrix realization of quantum loop algebras
PY  - 2022/05/04
UR  - https://www.scipost.org/SciPostPhys.12.5.146
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 12
IS  - 5
SP  - 146
A1  - Liashyk, Andrii
AU  - Pakuliak, Stanislav
AB  - We consider $\rm R$-matrix realization of the quantum deformations of the loop algebras $\tilde{\mathfrak{g}}$ corresponding to non-exceptional affine Lie algebras of type $\widehat{\mathfrak{g}}=A^{(1)}_{N-1}$, $B^{(1)}_n$, $C^{(1)}_n$, $D^{(1)}_n$, $A^{(2)}_{N-1}$. 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.
ER  -

@Article{10.21468/SciPostPhys.12.5.146,
	title={{On the R-matrix realization of quantum loop algebras}},
	author={A. Liashyk and S. Z. Pakuliak},
	journal={SciPost Phys.},
	volume={12},
	pages={146},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.12.5.146},
	url={https://scipost.org/10.21468/SciPostPhys.12.5.146},
}