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arXiv · 1702.08710

Highest $\ell$-Weight Representations and Functional Relations

Khazret S. Nirov·Alexander V. Razumov
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Abstract

We discuss highest $\ell$-weight representations of quantum loop algebras and the corresponding functional relations between integrability objects. In particular, we compare the prefundamental and $q$-oscillator representations of the positive Borel subalgebras of the quantum group $\mathrm{U}_q(\mathcal L(\mathfrak{sl}_{l+1}))$ for arbitrary values of $l$. Our article has partially the nature of a short review, but it also contains new results. These are the expressions for the $L$-operators, and the exact relationship between different representations, as a byproduct resulting in certain conclusions about functional relations.

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Khazret S. Nirov, Alexander V. Razumov. 2017-02-28. Highest $\ell$-Weight Representations and Functional Relations. https://doi.org/10.3842/sigma.2017.043

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