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 SIGMA, 2019, Volume 15, 089, 36 pages (Mi sigma1525)

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.

 Funding Agency Grant Number Agence Nationale de la Recherche ANR-15-CE40-0004-01 I also want to thank Luc Pirio for stimulating discussions on the subject. This work is supported by the ANR project $SC^3A$, ANR-15-CE40-0004-01.

DOI: https://doi.org/10.3842/SIGMA.2019.089

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Bibliographic databases:

ArXiv: 1803.06001
MSC: 13F60; 05E10; 14N20; 53D30
Received: June 18, 2019; in final form November 7, 2019; Published online November 14, 2019
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Citation: Sophie Morier-Genoud, “Symplectic Frieze Patterns”, SIGMA, 15 (2019), 089, 36 pp.

Citation in format AMSBIB
\Bibitem{Mor19}
\by Sophie~Morier-Genoud
\paper Symplectic Frieze Patterns
\jour SIGMA
\yr 2019
\vol 15
\papernumber 089
\totalpages 36
\mathnet{http://mi.mathnet.ru/sigma1525}
\crossref{https://doi.org/10.3842/SIGMA.2019.089}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85075121976}