Highest $\ell$-Weight Representations and Functional Relations

Symmetry Integrability and Geometry-Methods and Applications

article

Khazret S. Nirov¹  Alexander V. Razumov² 

[1] Institute for Nuclear Research of the Russian Academy of Sciences;Institute for High Energy Physics, NRC ''Kurchatov Institute''

关键词: quantum loop algebras;    Verma modules;    highest `-weight representations;    q-oscillators;   

DOI  :  10.3842/SIGMA.2017.043

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown