DOMINANCE ORDER AND MONOIDAL CATEGORIFICATION OF CLUSTER ALGEBRAS - Sorbonne Université
Journal Articles Pacific Journal of Mathematics Year : 2020

DOMINANCE ORDER AND MONOIDAL CATEGORIFICATION OF CLUSTER ALGEBRAS

Abstract

We study a compatibility relationship between Qin's dominance order on a cluster algebra A and partial orderings arising from classifications of simple objects in a monoidal categorification C of 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 n quiver Hecke algebra using Kleshchev-Ram's classification of irreducible finite-dimensional representations.
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Dates and versions

hal-02995947 , version 1 (09-11-2020)

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Elie Casbi. DOMINANCE ORDER AND MONOIDAL CATEGORIFICATION OF CLUSTER ALGEBRAS. Pacific Journal of Mathematics, 2020, 305 (2), pp.473-537. ⟨10.2140/pjm.2020.305.473⟩. ⟨hal-02995947⟩
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