  In this paper, we introduce an algebra $\mathcal{H}$ from a subspace lattice
with respect to a fixed flag which contains its incidence algebra as a proper
subalgebra. We then establish a relation between the algebra $\mathcal{H}$ and
the quantum affine algebra $U_{q^{1/2}}(\widehat{\mathfrak{sl}}_2)$, where $q$
denotes the cardinality of the base field. It is an extension of the well-known
relation between the incidence algebra of a subspace lattice and the quantum
algebra $U_{q^{1/2}}(\mathfrak{sl}_2)$. We show that there exists an algebra
homomorphism from $U_{q^{1/2}}(\widehat{\mathfrak{sl}}_2)$ to $\mathcal{H}$ and
that any irreducible module for $\mathcal{H}$ is irreducible as an
$U_{q^{1/2}}(\widehat{\mathfrak{sl}}_2)$-module.
