A Laurent Phenomenon for the Cayley Plane
Abstract
We describe a Laurent phenomenon for the Cayley plane, which is the homogeneous variety associated to the cominuscule representation of E6. The corresponding Laurent phenomenon algebra has finite type and appears in a natural sequence of LPAs indexed by the En Dynkin diagrams for n≤6. We conjecture the existence of a further finite type LPA, associated to the Freudenthal variety of type E7.
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