Oliver Daisey, Tom Ducat
Published 2023-10-16Version 1
We describe a Laurent phenomenon for the Cayley plane, which is the homogeneous variety associated to the cominiscule 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 $n \leq 6$. We conjecture the existence of a further finite type LPA, associated to the Freudenthal variety of type $E_7$.
Comments: 19 pages, 6 figures
On the derived category of the Cayley plane
Derived categories of the Cayley plane and the coadjoint Grassmannian of type F
Dynkin diagrams of rank 20 on supersingular K3 surfaces
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