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On the R-matrix realization of quantum loop algebras
by A. Liashyk, S. Z. Pakuliak
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Submission summary
| Authors (as registered SciPost users): | Stanislav Pakuliak |
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| Preprint Link: | https://arxiv.org/abs/2106.10666v3 (pdf) |
| Date accepted: | 2022-04-06 |
| Date submitted: | 2022-01-28 02:38 |
| Submitted by: | Pakuliak, Stanislav |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Mathematics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
List of changes
We include in the manuscript all corrections sent by Referee N2
Since the publication of the paper was rather delayed we changed the funding information and affiliations of one of the author
Published as SciPost Phys. 12, 146 (2022)