Highest $\ell$-Weight Representations and Functional Relations

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.

References in corpus (3)

• Oscillator versus prefundamental representations II. Arbitrary higher ranks
• Oscillator versus prefundamental representations
• Quantum groups, Verma modules and $q$-oscillators: General linear case

Cited by in corpus (2)

• Vertex Models and Spin Chains in Formulas and Pictures
• Quantum groups and functional relations for arbitrary rank