  Based on the work of Ringel and Green, one can define the (Drinfeld) double
Ringel--Hall algebra ${\mathscr D}(Q)$ of a quiver $Q$ as well as its highest
weight modules. The main purpose of the present paper is to show that the basic
representation $L(\Lambda_0)$ of ${\mathscr D}(\Delta_n)$ of the cyclic quiver
$\Delta_n$ provides a realization of the $q$-deformed Fock space
$\bigwedge^\infty$ defined by Hayashi. This is worked out by extending a
construction of Varagnolo and Vasserot. By analysing the structure of nilpotent
representations of $\Delta_n$, we obtain a decomposition of the basic
representation $L(\Lambda_0)$ which induces the Kashiwara--Miwa--Stern
decomposition of $\bigwedge^\infty$ and a construction of the canonical basis
of $\bigwedge^\infty$ defined by Leclerc and Thibon in terms of certain
monomial basis elements in ${\mathscr D}(\Delta_n)$.
