  The Lascoux-Leclerc-Thibon conjecture, reformulated and solved by S. Ariki,
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 the Lie algebra $gl_\infty$ or the affine
Lie algebra $A^{(1)}_\ell$, and the irreducible representations correspond to
the upper global bases. In this note, we formulate analogous conjectures for
certain classes of irreducible representations of affine Hecke algebras of type
B. We corrected typos.
