After a five-page introduction the antiplectic formalism is reviewed following the author [Q. J. Math., Oxf. II. Ser. 42, 227-256 (1991; Zbl 0755.58030)]. The so-called special 2-forms are introduced and comparisons with the standard Hamiltonian formalism are drawn. Several properties of the bilinear concomitant on a differential field are then examined. A tensor is defined and shown to be a closed special 2-form, which determines a Hamiltonian operator \(\ell\). Two spaces forming an antiplectic pair are then used to recover the Adler-Gel’fand-Dikij (AGD) bracket. The kernel of the AGD operator \(\ell\) is shown to be given by a generalization of the squared eigenfunctions of the Schrödinger case. In the final section the whole construction is regarded from the standpoint of loop groups.