Almost unramified automorphic representations for split groups over Fq(t)

Let G be a split semisimple group over a finite field Fq, F the field Fq(t) of rational functions in t with coefficients in Fq and A the adèles of F. We describe the irreducible automorphic representations of G(A) which have non-zero vectors invariant under Iwahori subgroups at two places and under maximal compact subgroups at all other places in terms of the irreducible square-integrable representations of an Iwahori–Hecke algebra associated to G and the Satake isomorphism.