REVIEW 1 cited by
On exchange matrices from string diagrams
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
Inspired by Fock-Goncharov's amalgamation procedure \cite{Fock-Goncharov-2006}, Shen-Weng introduced string diagrams in \cite{Shen-Weng-2021}, which are very useful to describe many interesting skew-symmetrizable matrices closely related with Lie theory. In this paper, we prove that the skew-symmetrizable matrices from string diagrams are in the smallest class $\mathcal P^\prime$ of skew-symmetrizable matrices containing the $1\times 1$ zero matrix and closed under mutations and source-sink extensions. This result applies to the exchange matrices of cluster algebras from double Bruhat cells, unipotent cells, double Bott-Samelson cells and so on. Our main result can be used to explain why many skew-symmetrizable matrices from Lie theory have reddening sequences. It can be also used to prove some interesting results regarding non-degenerate potentials on many quivers from Lie theory.
Forward citations
Cited by 1 Pith paper
-
Cluster Algebras for Bosonic Plethysm
For tuples of symmetric matrices, an explicit folded cluster seed gives the invariant ring and expresses symmetric-square plethysm coefficients as alternating sums of cone lattice point counts.
Discussion (0). Continue with ORCID to comment.