The author introduces a conjecture on the integral curves of a certain distribution on the flag manifold of a simple Lie group G. The case \(G=SU_{n+1}\) corresponds to the general Plücker formula [see P. Griffiths and J. Harris: “Principles of algebraic geometry” (1978; Zbl 0408.14001); p. 270]. The case \(G=Sp_{2n}\) leads to the Plücker formula for the autodual curves in \({\mathbb{P}}^{2n-1}\) whose definition uses the symplectic structure on \({\mathbb{C}}^{2n}\).