First symplectic Chern class and Maslov indices

An explicit formula is given in this paper for a two-dimensional cocycle in the bar resolution of the group $G=Sp(n,\mathbb R)$, which represents the first Chern class of the natural $n$-dimensional complex vector bundle over $BG^\delta$. It is shown that this cocycle is closely connected with the Maslov indices of Lagrangian subspaces of $\mathbb R^{2n}$.