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Regular version of the site

Article

Highest ℓ-weight representations and functional relations

Nirov Khazret S., Razumov A. V.

We discuss highest ℓ-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 Uq(L(sll+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.