Multiple commutation relations of the quantum affine algebra $U_q({\widehat{\mathfrak{gl}}}_N)$, nested Bethe vector and the Gelfand-Tsetlin basis

Allan John Gerrard, Kohei Motegi, Kazumitsu Sakai

We study a certain type of multiple commutation relations of the quantum affine algebra $U_q({\widehat{\mathfrak{gl}}}_N)$. We show that all the coefficients in the multiple commutat…