Symmetric Crystals for ${\mathfrak{gl}}_{\infty }$

Abstract

In the preceding paper, we formulated a conjecture on the relations between certain classes of irreducible representations of affine Hecke algebras of type B and symmetric crystals for ${\mathfrak{gl}}_{\infty }$. In the present paper, we prove the existence of the symmetric crystal and the global basis for ${\mathfrak{gl}}_{\infty }$.