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Symmetry, Integrability and Geometry: Methods and Applications, 2024, Volume 20, 033, 18 pp.
DOI: https://doi.org/10.3842/SIGMA.2024.033 (Mi sigma2035) 		 
A Laurent Phenomenon for the Cayley Plane

Oliver Daisey, Tom Ducat

Department of Mathematical Sciences, Durham University, Upper Mountjoy Campus, Stockton Road, Durham DH1 3LE, UK
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DOI: https://doi.org/10.3842/SIGMA.2024.033
Abstract: We describe a Laurent phenomenon for the Cayley plane, which is the homogeneous variety associated to the cominuscule representation of $E_6$. The corresponding Laurent phenomenon algebra has finite type and appears in a natural sequence of LPAs indexed by the $E_n$ Dynkin diagrams for $n\leq6$. We conjecture the existence of a further finite type LPA, associated to the Freudenthal variety of type $E_7$.
Keywords: Laurent phenomenon, cluster structure, mirror symmetry, Cayley plane.
Received: October 22, 2023; in final form April 11, 2024; Published online April 15, 2024
Document Type: Article
MSC: 13F60, 14M17
Language: English
Citation: Oliver Daisey, Tom Ducat, “A Laurent Phenomenon for the Cayley Plane”, SIGMA, 20 (2024), 033, 18 pp.
Citation in format AMSBIB
\Bibitem{DaiDuc24}
\by Oliver~Daisey, Tom~Ducat
\paper A Laurent Phenomenon for the Cayley Plane
\jour SIGMA
\yr 2024
\vol 20
\papernumber 033
\totalpages 18
\mathnet{http://mi.mathnet.ru/sigma2035}
\crossref{https://doi.org/10.3842/SIGMA.2024.033}
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