Cluster algebras and semi‐invariant rings I. Triple flags | Zendy

Fei Jiarui | Zendy

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Cluster algebras and semi‐invariant rings I. Triple flags

Author(s) -

Fei Jiarui

Publication year - 2017

Publication title -

proceedings of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.899

H-Index - 65

eISSN - 1460-244X

pISSN - 0024-6115

DOI - 10.1112/plms.12033

Subject(s) - mathematics , quiver , cluster algebra , invariant (physics) , flag (linear algebra) , pure mathematics , cluster (spacecraft) , combinatorics , algebra over a field , physics , computer science , mathematical physics , programming language , ising model , statistical physics

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 G n such that the generic cluster character maps its lattice points onto a basis of the upper cluster algebra. As an application, we use the cluster algebra structure to find a special minimal set of generators for these semi‐invariant rings when n is small.

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