  We consider moduli spaces of cyclic configurations of $N$ lines in a
$2n$-dimensional symplectic vector space, such that every set of $n$
consecutive lines generates a Lagrangian subspace. We study geometric and
combinatorial problems related to these moduli spaces, and prove that they are
isomorphic to quotients of spaces of symmetric linear difference operators with
monodromy $-1$.
  The symplectic cross-ratio is an invariant of two pairs of $1$-dimensional
subspaces of a symplectic vector space. For $N = 2n+2$, the moduli space of
Lagrangian configurations is parametrized by $n+1$ symplectic cross-ratios.
These cross-ratios satisfy a single remarkable relation, related to tridiagonal
determinants and continuants, given by the Pfaffian of a Gram matrix.
