Dirac structures for higher analogues of Courant algebroids

In this paper, we introduce the notion of a (p, k)-Dirac structure in TM circle plus Lambda T-p*M, where 0 <= k <= p - 1. The (p, 0)-Dirac structures are exactly the higher analogues of Dirac structures of order p introduced by Zambon in [L-infinity-algebras and higher analogues of Dirac structures and Courant algebroids, J. Symplectic Geom. 10(4) (2012) 563-599]. The (p, p - 1)-Dirac structures are exactly the Nambu-Dirac structures introduced by Hagiwara in [Nambu-Dirac manifolds, J. Phys. A 35(5) (2002) 1263-1281]. In the regular case, such a (p, k)-Dirac structure is characterized by a characteristic pair.