Tensor diagrams and cluster algebras

@article{Fomin2012TensorDA,
  title={Tensor diagrams and cluster algebras},
  author={Sergey Fomin and Pavlo Pylyavskyy},
  journal={arXiv: Combinatorics},
  year={2012}
}

Cluster Algebras and Classical Invariant Rings.

Let V be a k-dimensional complex vector space. The Plücker ring of polynomial SL(V ) invariants of a collection of n vectors in V can be alternatively described as the homogeneous coordinate ring of

Webs on surfaces, rings of invariants, and clusters

TLDR
Cluster algebra structures in classical rings of invariants for the special linear group SL3 are investigated and constructed using Kuperberg’s calculus of webs on marked surfaces with boundary.

Tensor diagrams and cluster combinatorics at punctures

Fock and Goncharov introduced a family of cluster algebras associated with the moduli of SLk-local systems on a marked surface with extra decorations at marked points. We study this family from an

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We prove that each semi‐invariant ring of the complete triple flag of length n is an upper cluster algebra associated to an ice hive quiver. We find a rational polyhedral cone Gn such that the

Graded quantum cluster algebras and an application to quantum Grassmannians

We introduce a framework for Z ‐gradings on cluster algebras (and their quantum analogues) that are compatible with mutation. To do this, one chooses the degrees of the (quantum) cluster variables in

Braid group symmetries of Grassmannian cluster algebras

We define an action of the extended affine d-strand braid group on the open positroid stratum in the Grassmannian Gr(k,n), for d the greatest common divisor of k and n. The action is by

Tropical Fock-Goncharov coordinates for SL3-webs on surfaces I: construction

For a finite-type surface S, we study a preferred basis for the commutative algebra C[RSL3(C)(S)] of regular functions on the SL3(C)-character variety, introduced by Sikora-Westbury. These basis

Quasi-homomorphisms of cluster algebras

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