Unipotent Quantum Coordinate Ring and Prefundamental Representations for Types A⁽¹⁾_n and D⁽¹⁾_n

We give a new realization of the prefundamental representations L^±_r,a introduced by Hernandez and Jimbo, when the quantum loop algebra U_q(g) is of types A⁽¹⁾_n and D⁽¹⁾_n and the r-th fundamental weight (Equation presented)r for types A_n and D_n is minuscule. We define an action of the Borel subalgebra U_q(b) of U_q(g) on the unipotent quantum coordinate ring associated to the translation by -(Equation presented)r and show that it is isomorphic to L^±_r,a. We then give a combinatorial realization of L⁺_r,a in terms of the Lusztig data of the dual PBW vectors.