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Lagrangian configurations and symplectic cross-ratios
- Source :
- Mathematische Annalen, Mathematische Annalen, Springer Verlag, In press, ⟨10.1007/s00208-019-01866-9⟩
- Publication Year :
- 2019
- Publisher :
- HAL CCSD, 2019.
-
Abstract
- 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.<br />Comment: 29 pages, minor revisions and corrections
- Subjects :
- Mathematics - Differential Geometry
Pure mathematics
Tridiagonal matrix
General Mathematics
010102 general mathematics
Pfaffian
Dynamical Systems (math.DS)
01 natural sciences
Linear subspace
Moduli space
Symplectic vector space
Differential Geometry (math.DG)
0103 physical sciences
FOS: Mathematics
010307 mathematical physics
Mathematics - Dynamical Systems
0101 mathematics
Invariant (mathematics)
[MATH]Mathematics [math]
Mathematics::Symplectic Geometry
ComputingMilieux_MISCELLANEOUS
Symplectic geometry
Gramian matrix
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 00255831 and 14321807
- Database :
- OpenAIRE
- Journal :
- Mathematische Annalen, Mathematische Annalen, Springer Verlag, In press, ⟨10.1007/s00208-019-01866-9⟩
- Accession number :
- edsair.doi.dedup.....d336e3fe9e8308bc11ba1de40e4a22ea