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arXiv · 2310.10223

A Laurent Phenomenon for the Cayley Plane

Oliver Daisey·Tom Ducat
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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 $E_7$.

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Oliver Daisey, Tom Ducat. 2023-10-16. A Laurent Phenomenon for the Cayley Plane. https://doi.org/10.3842/sigma.2024.033

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