The modular automorphisms of the Drinfeld modular curve \(X_1(\mathfrak n)\) (Q1423828)

Let \(q\) be a prime power, \(A = \mathbb{F}_q[T]\) be the polynomial ring in one indeterminate and \(\mathfrak{n}\) be an ideal of \(A\). In the present paper, the author determines the structure of the modular automorphisms of the Drinfeld modular curve \(X_1(\mathfrak{n})\). The main result states that the group of modular automorphisms is either: a) a generalized dihedral group \((A/\mathfrak{n})^{*}/\mathbb{F}_q^{*} \rtimes (\mathbb{Z}/2\mathbb{Z})\) if \(q \geq 3\); or b) an extension of \((A/\mathfrak{n})^{*}/\mathbb{F}_q^{*}\) by \((\mathbb{Z}/2 \mathbb{Z})^n\) if \(q = 2\) and \(\#(A/\mathfrak{n})^{*} \geq 2\), and \((\mathbb{Z}/2 \mathbb{Z})^n\) if \(q = 2\) and \(\mathfrak{n} = T\), \(T+1\) or \(T(T+1)\) (here \(n\) is the number of different prime divisors of \(\mathfrak{n}\)).