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arXiv · 1810.00970

Dominance order and monoidal categorification of cluster algebras

Elie Casbi
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Abstract

We study a compatibility relationship between Qin's dominance order on a cluster algebra $\mathcal{A}$ and partial orderings arising from classifications of simple objects in a monoidal categorification $\mathcal{C}$ of $\mathcal{A}$. Our motivating example is Hernandez-Leclerc's monoidal categorification using representations of quantum affine algebras. In the framework of Kang-Kashiwara-Kim-Oh's monoidal categorification via representations of quiver Hecke algebras, we focus on the case of the category $R-gmod$ for a symmetric finite type $A$ quiver Hecke algebra using Kleshchev-Ram's classification of irreducible finite dimensional representations.

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Elie Casbi. 2018-10-01. Dominance order and monoidal categorification of cluster algebras. https://doi.org/10.2140/pjm.2020.305.473

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