Lagrangian configurations and symplectic cross-ratios
| Autor: | Conley, Charles, Ovsienko, Valentin |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Math. Ann. 375 (2019) 1105-1145 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00208-019-01866-9 |
| Popis: | 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. Comment: 29 pages, minor revisions and corrections |
| Databáze: | arXiv |
| Externí odkaz: |
|