We give a proof of the cyclicity conjecture of Akasaka and Kashiwara for simply laced types, via quiver varieties. We also get an algebraic characterization of the standard modules.
"Standard modules of quantum affine algebras." Duke Math. J. 111 (3) 509 - 533, 15 February 2002. https://doi.org/10.1215/S0012-7094-02-11135-1