We consider reduced imaginary Verma modules for the untwisted quantum affine algebras Uq(gampersand-flag-changecirc;) and define a crystal-like base which we call imaginary crystal base using the Kashiwara algebra Kq constructed in earlier work by Ben Cox and two of the authors. We prove the existence of the imaginary crystal base for any object in a suitable category Ored,imq containing the reduced imaginary Verma modules for Uq(gampersand-flag-changecirc;).
