A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra

Mark J. Hopkins, Alexander I. Molev

We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra ${\mathrm{U}}_q({\widehat{\mathfrak{gl}}}_n)$. We then use it to give an explicit realiz…