A family of Hecke eigenforms for Drinfeld modular forms of arbitrary rank

We aim to provide a family of Drinfeld-Hecke eigenforms given in terms of a determinant of twisted Eisenstein series. Our main tool is the theory of vectorial Drinfeld modular forms, previously introduced by Pellarin [18] and extensively studied by Pellarin [19] as well as in his joint work with Perkins [20] in the rank two setting. We will develop this theory in the present paper for the arbitrary rank setting by using a particular representation.