Green walks in a hypergraph

Wolfgang Rump

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Let $Λ$ be a preprojective algebra of type $A, D, E$ , and let $G$ be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories $Sub Q$ for $Q$ an injective $Λ$ -module, and we introduce a mutation operation between complete rigid modules in $Sub Q$ . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to $G$ .

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