The automorphism group of the generalized Giulietti-Korchmaros function field

The Giulietti-Korchmros (GK) function field is the first example of a maximal function field which is not a subfield of the Hermitian function field over the same constant field. The generalized GK function field C-n was later introduced by Garcia, Guneri and Stichtenoth and was shown to be maximal too. In the present article we determine the automorphism group of the generalized GK function field. We prove that all the automorphisms of C-n fix the unique rational place at infinity and they are exactly the lifts of automorphisms of the Hermitian subfield H-n subset of C-n which fix the infinite place of H-n.