  The Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the
representations of the affine Hecke algebras of type A is isomorphic to the
algebra of functions on the maximal unipotent subgroup of the group associated
with a Lie algebra $g$ where $g$ is $gl_\infty$ or the affine Lie algebra
$A^{(1)}_\ell$, and the irreducible representations correspond to the upper
global bases. Recently, N. Enomoto and the first author presented the notion of
symmetric crystals and formulated analogous conjectures for the affine Hecke
algebras of type B. In this note, we present similar conjectures for certain
classes of irreducible representations of affine Hecke algebras of type D. The
crystal for type D is a double cover of the one for type B.
