Combinatorial model for m-cluster categories in type E
Bing Duan, Lisa Lamberti, Jian-Rong Li
TL;DR
This paper extends the geometric model of cluster categories in type E to m-cluster categories, linking colored diagonals to Young tableaux and providing new compatibility descriptions in Grassmannian cluster algebras.
Contribution
It generalizes the geometric description of type E cluster categories to m-cluster categories and connects colored diagonals with semi-standard Young tableaux in specific types.
Findings
Established a geometric model for m-cluster categories in type E.
Linked colored diagonals to semi-standard Young tableaux in types E_6, E_7, E_8.
Provided new compatibility criteria for tableaux in Grassmannian cluster algebras.
Abstract
We revisit the geometric description of cluster categories in type E in terms of colored diagonals in a polygon and generalize it to the case of m-cluster categories. As an application, we relate colored diagonals in a polygon to semi-standard Young tableaux, in type E_6,E_7,E_8. This provides a new compatibility description of semi--standard Young tableaux in Grassmannian cluster algebras in type E_6, E_8 and in a sub-cluster algebra of type E_7.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry