Gelfand-Zetlin basis for Uq(gl(N+1)) modules

Construction of Gelfand–Tsetlin Basis for $\mathcal U_q(\textit{gl}(N+1))$-modules

“…With this * structure, the module V(q< 1/2:>A ) turns out to be unitary [1]. Further {\fi> = l/N fl \fjt>} is an orthonormal basis, and the action of <U g on this basis is the same as the result of Jimbo [5].…”

“…In the previous paper [1], we constructed the Gelfand-Tsetlin basis for irreducible "Ug(^/(]V+l))-modules of finite dimensions, in terms of the lowering operators. In this paper, we will give detailed accounts of our construction of this basis.…”

On irreducibility of tensor products of evaluation modules for the quantum affine algebra

“…Here we modify the arguments of [17] to give q-analogs of the quantum minor formulas and construct a basis of GelfandTsetlin-type for the U q (gl n )-module L(λ). Some other constructions of such bases can be found in [12], [21], [26], [27]. A pattern Λ (associated with λ) is a sequence of rows of integers Λ n , Λ n−1 , .…”

Representations of Uq(sl(N)) at roots of unity

“…In [19][20][21][22], explicit expressions for usual representations of U q (sl(N )) are written, which lead when the deformation parameter q goes to a root of unity to either irreducible or reducible (sometimes not totally reducible) representations, depending on their highest weight [6,21,23].…”