This article is cited in 1 paper

Symplectic Frieze Patterns

Sophie Morier-Genoud

Sorbonne Université, Université Paris Diderot, CNRS, Institut de Mathé-matiquesde Jussieu-Paris Rive Gauche, IMJ-PRG, F-75005, Paris, France

Abstract: We introduce a new class of friezes which is related to symplectic geometry. On the algebraic and combinatrics sides, this variant of friezes is related to the cluster algebras involving the Dynkin diagrams of type $\mathrm{C}_{2}$ and $\mathrm{A}_{m}$. On the geometric side, they are related to the moduli space of Lagrangian configurations of points in the 4-dimensional symplectic space introduced in [Conley C.H., Ovsienko V., Math. Ann. 375 (2019), 1105–1145]. Symplectic friezes share similar combinatorial properties to those of Coxeter friezes and $\mathrm{SL}$-friezes.

Keywords: frieze, cluster algebra, moduli space, difference equation, Lagrangian configuration.

MSC: 13F60; 05E10; 14N20; 53D30

Received: June 18, 2019; in final form November 7, 2019; Published online November 14, 2019

Language: English

DOI: 10.3842/SIGMA.2019.089

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ArXiv: 1803.06001