  In the previous paper "Symmetric Crystals and Affine Hecke Algebras of Type
B", we formulated a conjecture on the relations between certain classes of
irreducible representations of affine Hecke algebras of type B and symmetric
crystals for $\gl_\infty$. In the first half of this paper (sections 2 and 3),
we give a survey of the LLTA type theorem of the affine Hecke algebra of type
$A$. In the latter half (sections 4, 5 and 6), we review the construction of
the symmetric crystals and the LLTA type conjectures for the affine Hecke
algebra of type $B$.
