Webs on surfaces, rings of invariants, and clusters
Sergey Fomin, Pavlo Pylyavskyy
TL;DR
This paper develops cluster algebra structures within rings of invariants for SL(3) acting on vectors, covectors, and matrices, utilizing Kuperberg's web calculus on marked surfaces.
Contribution
It introduces a novel construction of cluster algebra structures in invariant rings using web calculus on surfaces, linking algebraic invariants with geometric combinatorics.
Findings
Cluster structures are established in rings of invariants for SL(3).
Web calculus on surfaces provides a new framework for understanding invariants.
The approach connects algebraic invariants with geometric surface combinatorics.
Abstract
We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of three-dimensional vectors, covectors, and matrices. The construction uses Kuperberg's calculus of webs on marked surfaces with boundary.
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