# On the R-matrix realization of quantum loop algebras

### Submission summary

 Authors (as Contributors): Stanislav Pakuliak
Submission information
Date accepted: 2022-04-06
Date submitted: 2022-01-28 02:38
Submitted by: Pakuliak, Stanislav
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Mathematical Physics
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.

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

### Submission & Refereeing History

Resubmission 2106.10666v3 on 28 January 2022
Submission 2106.10666v1 on 23 June 2021

## Reports on this Submission

### 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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