In this article, we construct
-friezes
using Plücker coordinates, making use of the cluster structure
on the homogeneous coordinate ring of the Grassmannian of
-spaces in
-space
via the Plücker embedding. When this cluster algebra is of finite type, the
-friezes
are in bijection with the so-called mesh friezes of the corresponding
Grassmannian cluster category. These are collections of positive integers
on the AR-quiver of the category with relations inherited from the
mesh relations on the category. In these finite type cases, many of the
-friezes
arise from specializing a cluster to 1. These are called unitary. We use
Iyama–Yoshino reduction to analyze the nonunitary friezes. With this, we
provide an explanation for all known friezes of this kind. An appendix
by Cuntz and Plamondon proves that there are 868 friezes of type
.
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