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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 Contributors): Stanislav Pakuliak
Submission information
Arxiv Link: (pdf)
Date accepted: 2022-04-06
Date submitted: 2022-01-28 02:38
Submitted by: Pakuliak, Stanislav
Submitted to: SciPost Physics
Ontological classification
Academic field: Mathematics
  • Mathematical Physics
Approach: Theoretical


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.

Published as SciPost Phys. 12, 146 (2022)

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

Reports on this Submission

Anonymous Report 1 on 2022-2-20 (Invited Report)


I would like to thank the authors for taking care of my suggestions. I have no further suggestions/comments. The paper deserves to be published.

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