Automorphic representations and harmonic cochains for $G{L}_{n+1}$

Let $K$ be a global field of positive characteristic. Let $\mathrm{\infty }$ be a fixed place of $K$. This paper gives an explicit isomorphism between the space of automorphic forms (resp. cusp forms) for $G{L}_{n+1}(K)$ that transform like the special representations and certain spaces of harmonic cochains (resp. those with finite support) defined on the Bruhat-Tits building of $G{L}_{n+1}(K_{\mathrm{\infty }})$.